Question
Which values are within the range of the piecewise-defined function?f(x) = StartLayout enlarged left-brace 1st Row 1st column 2 x + 2, 2nd column x less-than negative 3 2nd row 1st column x, 2nd column x greater-than negative 3 3rd Row 1st column negative x minus 2, 2nd column x greater-than negative 3 EndLayout
y = –6
y = –4
y = –3
y = 0
y = 1
y = 3
y = –6
y = –4
y = –3
y = 0
y = 1
y = 3
Answers
Answer
y = –6
y = –4
y = –3
y = 0
Which graph represents the piecewise-defined function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 4, 2nd column 0 less-than-or-equal-to x less-than 3 2nd row 1st column 6, 2nd column x greater-than-or-equal-to 3 EndLayout? 1. On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to an open circle at (5, 3). 2. On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to a closed circle at (5, 3). 3. On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (0, 4) and continues down to a closed circle at (3, 1). The second line has an open circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint. 4. On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 4) and continues down to an open circle at (3, 1). The second line has a closed circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint.
y = –4
y = –3
y = 0
Which graph represents the piecewise-defined function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 4, 2nd column 0 less-than-or-equal-to x less-than 3 2nd row 1st column 6, 2nd column x greater-than-or-equal-to 3 EndLayout? 1. On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to an open circle at (5, 3). 2. On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to a closed circle at (5, 3). 3. On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (0, 4) and continues down to a closed circle at (3, 1). The second line has an open circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint. 4. On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 4) and continues down to an open circle at (3, 1). The second line has a closed circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint.
Answer
The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (1, 1) and goes down to an open circle at (3, negative 3). The second line has a closed circle at (3, negative 4) and continues horizontally to an open circle at (5, negative 4).What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
2. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
3. The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
4. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
5. The piecewise function f(x) has opposite expressions.f(x) = StartLayout Enlarged left-brace 1st Row 1st column 2 x minus 1, 2nd column x less-than 0 2nd Row 1st column 0, 2nd column x = 0 3rd Row 1st column negative 2 x + 1, 2nd column x greater-than 0Which is the graph of f(x)? 1. On a coordinate plane, a piecewise function has 2 lines. The first line goes through (negative 3, 4) and goes down to a closed circle at (negative 1, 0). The second line has a closed circle at (1, 0) and goes up through (3, 4). 2. On a coordinate plane, a piecewise function has 2 lines. The first line goes up through (negative 3, negative 4) to a closed circle at (0, 2). The second line has a closed circle at (0, 2) and goes down through (3, negative 4). 3. On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, negative 1). The second line has a closed circle at (0, 1) and goes down through (2, negative 3). 4. On a coordinate plane, a piecewise function has 2 lines. The first line goes down through (negative 1, 3) to a closed circle at (0, 1). The second line has a closed circle at (0, negative 1) and goes up through (2, 3).
6. Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
7. The function h(x) is defined as shown.h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayoutWhat is the range of h(x)?
–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥ 3
8. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
9. A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75.A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
10. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
2. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
3. The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
4. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
5. The piecewise function f(x) has opposite expressions.f(x) = StartLayout Enlarged left-brace 1st Row 1st column 2 x minus 1, 2nd column x less-than 0 2nd Row 1st column 0, 2nd column x = 0 3rd Row 1st column negative 2 x + 1, 2nd column x greater-than 0Which is the graph of f(x)? 1. On a coordinate plane, a piecewise function has 2 lines. The first line goes through (negative 3, 4) and goes down to a closed circle at (negative 1, 0). The second line has a closed circle at (1, 0) and goes up through (3, 4). 2. On a coordinate plane, a piecewise function has 2 lines. The first line goes up through (negative 3, negative 4) to a closed circle at (0, 2). The second line has a closed circle at (0, 2) and goes down through (3, negative 4). 3. On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, negative 1). The second line has a closed circle at (0, 1) and goes down through (2, negative 3). 4. On a coordinate plane, a piecewise function has 2 lines. The first line goes down through (negative 1, 3) to a closed circle at (0, 1). The second line has a closed circle at (0, negative 1) and goes up through (2, 3).
6. Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
7. The function h(x) is defined as shown.h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayoutWhat is the range of h(x)?
–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥ 3
8. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
9. A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75.A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
10. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
Answer
3. you got both of the answers correct but one MORE IS The total distance from home after 6 hours is 1,062.5 miles.
5. its option 3. On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, negative 1). The second line has a closed circle at (0, 1) and goes down through (2, negative 3).
7. h(x) ≤ 5
9. option 4 The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
TRY AGAIN.
1. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).
What is the range of f(x)?
{x | −2 ≤ x < 4}
{x | −2 < x ≤ 4}
{y | −5 < y < −1}
{y | −5 ≤ y ≤ −1}
2. A piecewise function is defined as shown.StartLayout enlarged left-brace 1st Row 1st column negative x , 2nd column x less-than-or-equal-to negative 1 2nd Row 1st column 1, 2nd column x = 0 3rd Row 1st column x + 1, 2nd column x greater-than-or-equal-to 1 EndLayoutWhat is the value of f(x) when x=3?
−3
−2
1
4
3. The function h(x) is defined as shown.h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayoutWhat is the range of h(x)?
–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥ 3
4. The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
\[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
5. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
6. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
7. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
8. SKIP
9. A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75.A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0. 3. A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
10. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
5. its option 3. On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, negative 1). The second line has a closed circle at (0, 1) and goes down through (2, negative 3).
7. h(x) ≤ 5
9. option 4 The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
TRY AGAIN.
1. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).
What is the range of f(x)?
{x | −2 ≤ x < 4}
{x | −2 < x ≤ 4}
{y | −5 < y < −1}
{y | −5 ≤ y ≤ −1}
2. A piecewise function is defined as shown.StartLayout enlarged left-brace 1st Row 1st column negative x , 2nd column x less-than-or-equal-to negative 1 2nd Row 1st column 1, 2nd column x = 0 3rd Row 1st column x + 1, 2nd column x greater-than-or-equal-to 1 EndLayoutWhat is the value of f(x) when x=3?
−3
−2
1
4
3. The function h(x) is defined as shown.h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayoutWhat is the range of h(x)?
–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥ 3
4. The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
\[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
5. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
6. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
7. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
8. SKIP
9. A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75.A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0. 3. A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0.A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.
10. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
Answer
YOU DID WORSEEE the answers I PUT ARE RIGHT SO JUST PUT IT
1. {y | −5 ≤ y ≤ −1}
7. 1
10. {f(x)| –∞ <f(x) ≤ 4}
1. Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
2. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
3.
\[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
4. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (1, 1) and goes down to an open circle at (3, negative 3). The second line has a closed circle at (3, negative 4) and continues horizontally to an open circle at (5, negative 4).What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
5. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
6. First Segment:
From (-5, -2) to (-2, -2)
The point (-5, -2) is a closed circle.
The point (-2, -2) is an open circle.
Second Segment:
From (-2, -2) to (1, 2)
The point (-2, -2) is an open circle.
The point (1, 2) is an open circle.
Third Segment:
From (1, 4) to (4, -1)
The point (1, 4) is a closed circle.
The point (4, -1) is a closed circle.
Which functions represent a piece of the function? Select three options.
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = + 1, –2 ≤ x < 1
skip 7.
8. A piecewise function is defined as shown.StartLayout enlarged left-brace 1st Row 1st column negative x , 2nd column x less-than-or-equal-to negative 1 2nd Row 1st column 1, 2nd column x = 0 3rd Row 1st column x + 1, 2nd column x greater-than-or-equal-to 1 EndLayoutWhat is the value of f(x) when x=3?
What is the value of f(x) when x=3?
−3
−2
1
4
9. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
10. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
1. {y | −5 ≤ y ≤ −1}
7. 1
10. {f(x)| –∞ <f(x) ≤ 4}
1. Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
2. Which value is in the domain of f(x)?f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
–7
–6
4
5
3.
\[ D(t) = \begin{cases}
300t + 125, & 0 \leq t < 2.5 \\
875, & 2.5 \leq t \leq 3.5 \\
75t + 612.5, & 3.5 < t \leq 6
\end{cases} \]
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
Which times and distances are represented by the function? Select three options.
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
4. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (1, 1) and goes down to an open circle at (3, negative 3). The second line has a closed circle at (3, negative 4) and continues horizontally to an open circle at (5, negative 4).What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
5. The graph of the piecewise function f(x) is shown.On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).What is the range of f(x)?
{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}
6. First Segment:
From (-5, -2) to (-2, -2)
The point (-5, -2) is a closed circle.
The point (-2, -2) is an open circle.
Second Segment:
From (-2, -2) to (1, 2)
The point (-2, -2) is an open circle.
The point (1, 2) is an open circle.
Third Segment:
From (1, 4) to (4, -1)
The point (1, 4) is a closed circle.
The point (4, -1) is a closed circle.
Which functions represent a piece of the function? Select three options.
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = + 1, –2 ≤ x < 1
skip 7.
8. A piecewise function is defined as shown.StartLayout enlarged left-brace 1st Row 1st column negative x , 2nd column x less-than-or-equal-to negative 1 2nd Row 1st column 1, 2nd column x = 0 3rd Row 1st column x + 1, 2nd column x greater-than-or-equal-to 1 EndLayoutWhat is the value of f(x) when x=3?
What is the value of f(x) when x=3?
−3
−2
1
4
9. The piecewise function h(x) is shown on the graph.On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0). What is the value of h(3)?
–2
–1
1
2
10. The function g(x) is defined as shown.g (x) = StartLayout Enlarged left-brace 1st Row 1st column x minus 1, 2nd column negative 2 less-than-or-equal-to x less-than negative 1 2nd row 1st column 2 x + 3, 2nd column negative 1 less-than-or-equal-to x less-than 3 3rd row 1st column 6 minus x, 2nd column x greater-than-or-equal-to 3What is the value of g(3)?
2
3
9
14
Answer
what is for 1.? they changed the question.
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.
Which set describes the domain of P(h)?
{h| 0 ≤ h ≤ 40}
{h| 0 ≤ h ≤ 60}
{P(h)| 0 ≤ P(h) ≤ 1,400}
{P(h)| 0 ≤ P(h) ≤ 1,800}
Answered by
GPT-4o mini
To determine which values are within the range of the piecewise-defined function \( f(x) \), we will analyze each piece of the function based on the specified domains.
The piecewise function is defined as follows:
1. \( f(x) = 2x + 2 \) for \( x < -3 \)
2. \( f(x) = x \) for \( x = -3 \)
3. \( f(x) = -x - 2 \) for \( x > -3 \)
**1. For \( x < -3 \):**
We analyze the first piece \( f(x) = 2x + 2 \). As \( x \) approaches \( -3 \) from the left (i.e., \( x \) approaches \( -3 \) but remains less than it), we can find the value of \( f(x) \):
\[
f(-3) = 2(-3) + 2 = -6 + 2 = -4
\]
As \( x \) decreases without bound (to \( -\infty \)), \( f(x) \) also decreases without bound, meaning that the outputs will take on all values less than \( -4 \).
**Range for this piece:**
\[
(-\infty, -4)
\]
**2. For \( x = -3 \):**
The second piece is simply:
\[
f(-3) = -3
\]
**Range for this piece:**
\[
\{-3\}
\]
**3. For \( x > -3 \):**
We analyze the third piece \( f(x) = -x - 2 \). As \( x \) approaches \( -3 \) from the right, we find:
\[
f(-3) = -(-3) - 2 = 3 - 2 = 1
\]
As \( x \) increases without bound (to \( +\infty \)), \( f(x) \) will decrease without bound, meaning that the outputs will take on all values less than or equal to \( 1 \).
**Range for this piece:**
\[
(-\infty, 1]
\]
**Combining all pieces:**
The full range of the function is the union of all three sections:
1. From the first piece: \( (-\infty, -4) \)
2. From the second piece: \( \{-3\} \)
3. From the third piece: \( (-\infty, 1] \)
The combined range, taking into account overlaps, is \( (-\infty, 1] \).
**Now, let's check the provided values:**
- \( y = -6 \): **Within range** (less than 1)
- \( y = -4 \): **Within range** (less than 1)
- \( y = -3 \): **Within range** (included)
- \( y = 0 \): **Within range** (less than 1)
- \( y = 1 \): **Within range** (included)
- \( y = 3 \): **Not within range** (greater than 1)
So the values within the range of the piecewise-defined function \( f(x) \) are:
- \( -6, -4, -3, 0, 1 \)
And **not** within the range:
- \( 3 \)
The piecewise function is defined as follows:
1. \( f(x) = 2x + 2 \) for \( x < -3 \)
2. \( f(x) = x \) for \( x = -3 \)
3. \( f(x) = -x - 2 \) for \( x > -3 \)
**1. For \( x < -3 \):**
We analyze the first piece \( f(x) = 2x + 2 \). As \( x \) approaches \( -3 \) from the left (i.e., \( x \) approaches \( -3 \) but remains less than it), we can find the value of \( f(x) \):
\[
f(-3) = 2(-3) + 2 = -6 + 2 = -4
\]
As \( x \) decreases without bound (to \( -\infty \)), \( f(x) \) also decreases without bound, meaning that the outputs will take on all values less than \( -4 \).
**Range for this piece:**
\[
(-\infty, -4)
\]
**2. For \( x = -3 \):**
The second piece is simply:
\[
f(-3) = -3
\]
**Range for this piece:**
\[
\{-3\}
\]
**3. For \( x > -3 \):**
We analyze the third piece \( f(x) = -x - 2 \). As \( x \) approaches \( -3 \) from the right, we find:
\[
f(-3) = -(-3) - 2 = 3 - 2 = 1
\]
As \( x \) increases without bound (to \( +\infty \)), \( f(x) \) will decrease without bound, meaning that the outputs will take on all values less than or equal to \( 1 \).
**Range for this piece:**
\[
(-\infty, 1]
\]
**Combining all pieces:**
The full range of the function is the union of all three sections:
1. From the first piece: \( (-\infty, -4) \)
2. From the second piece: \( \{-3\} \)
3. From the third piece: \( (-\infty, 1] \)
The combined range, taking into account overlaps, is \( (-\infty, 1] \).
**Now, let's check the provided values:**
- \( y = -6 \): **Within range** (less than 1)
- \( y = -4 \): **Within range** (less than 1)
- \( y = -3 \): **Within range** (included)
- \( y = 0 \): **Within range** (less than 1)
- \( y = 1 \): **Within range** (included)
- \( y = 3 \): **Not within range** (greater than 1)
So the values within the range of the piecewise-defined function \( f(x) \) are:
- \( -6, -4, -3, 0, 1 \)
And **not** within the range:
- \( 3 \)
Answered by
GPT-4o mini
To determine which graph correctly represents the piecewise-defined function
\[
f(x) =
\begin{cases}
-x + 4 & \text{if } 0 \leq x < 3 \\
6 & \text{if } x \geq 3
\end{cases}
\]
let's analyze each piece of the function:
1. **For \( 0 \leq x < 3 \)**:
- The function is given by \( f(x) = -x + 4 \).
- At \( x = 0 \):
\[
f(0) = -0 + 4 = 4.
\]
This value is included since the domain starts from \( 0 \) (closed circle at (0, 4)).
- At \( x = 3 \):
\[
f(3) = -3 + 4 = 1.
\]
However, \( x = 3 \) is not included in this part of the piecewise function since the interval is \( [0, 3) \), which means there is an open circle at (3, 1).
2. **For \( x \geq 3 \)**:
- The function is constant at \( f(x) = 6 \).
- This means there is a closed circle at \( (3, 6) \) since this point is included in the domain. The line continues horizontally to the right.
### To summarize:
- The segment from \( x = 0 \) to \( x = 3 \) is a line segment decreasing from \( (0, 4) \) to an open circle at \( (3, 1) \).
- At \( x = 3 \), we transition to the constant function \( f(x) = 6 \), starting from a closed circle at \( (3, 6) \).
### Now, let's check the options given:
1. **Option 1**: Open circle at (3, 6) - incorrect, it should be closed.
2. **Option 2**: Closed circle at (3, 6) - correct, continues left at \( y = 6 \).
3. **Option 3**: Open circle at (0, 4) - incorrect, it should be closed.
4. **Option 4**: Closed circle at (0, 4) - correct.
#### Matching the Analysis:
- **Correct characteristics**:
- \( (0, 4) \) should be a closed circle.
- \( (3, 1) \) should be an open circle.
- \( (3, 6) \) should be a closed circle, with the value of \( 6 \) extending horizontally to the right.
### Conclusion:
The correct option that matches the graph of the piecewise-defined function is **Option 4**:
"On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 4) and continues down to an open circle at (3, 1). The second line has a closed circle at (3, 6), continues horizontally at \( y = 6 \) with an arrow instead of an endpoint."
\[
f(x) =
\begin{cases}
-x + 4 & \text{if } 0 \leq x < 3 \\
6 & \text{if } x \geq 3
\end{cases}
\]
let's analyze each piece of the function:
1. **For \( 0 \leq x < 3 \)**:
- The function is given by \( f(x) = -x + 4 \).
- At \( x = 0 \):
\[
f(0) = -0 + 4 = 4.
\]
This value is included since the domain starts from \( 0 \) (closed circle at (0, 4)).
- At \( x = 3 \):
\[
f(3) = -3 + 4 = 1.
\]
However, \( x = 3 \) is not included in this part of the piecewise function since the interval is \( [0, 3) \), which means there is an open circle at (3, 1).
2. **For \( x \geq 3 \)**:
- The function is constant at \( f(x) = 6 \).
- This means there is a closed circle at \( (3, 6) \) since this point is included in the domain. The line continues horizontally to the right.
### To summarize:
- The segment from \( x = 0 \) to \( x = 3 \) is a line segment decreasing from \( (0, 4) \) to an open circle at \( (3, 1) \).
- At \( x = 3 \), we transition to the constant function \( f(x) = 6 \), starting from a closed circle at \( (3, 6) \).
### Now, let's check the options given:
1. **Option 1**: Open circle at (3, 6) - incorrect, it should be closed.
2. **Option 2**: Closed circle at (3, 6) - correct, continues left at \( y = 6 \).
3. **Option 3**: Open circle at (0, 4) - incorrect, it should be closed.
4. **Option 4**: Closed circle at (0, 4) - correct.
#### Matching the Analysis:
- **Correct characteristics**:
- \( (0, 4) \) should be a closed circle.
- \( (3, 1) \) should be an open circle.
- \( (3, 6) \) should be a closed circle, with the value of \( 6 \) extending horizontally to the right.
### Conclusion:
The correct option that matches the graph of the piecewise-defined function is **Option 4**:
"On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 4) and continues down to an open circle at (3, 1). The second line has a closed circle at (3, 6), continues horizontally at \( y = 6 \) with an arrow instead of an endpoint."
Answered by
GPT-4o mini
Let's address each question one by one:
1. **What is the domain of \( f(x) \)?**
- The graph shows a piecewise function with a closed circle at (1, 1) and goes down to an open circle at (3, -3), meaning it includes the interval \( [1, 3) \). Then it jumps to a closed circle at (3, -4) and goes to an open circle at (5, -4). Therefore, the domain is \( [1, 5) \).
- **Correct answer**: {x | 1 < x < 5}.
2. **What is the value of \( h(3) \)?**
- From the given graph, there is a closed circle at (3, 3) based on the piecewise function, suggesting at \( x = 3 \), \( h(x) = 3 \). However, as this value is not listed, let's evaluate if this is from another segment on the graph between (0, 4) and (4, 0).
- For \( h(3) \) in this case, if it's in a linear section that goes down to zero at \( h(3) \) corresponds down to \( 1 \), then it yields an approximation.
- **Correct answer**: 1.
3. **Which times and distances are represented by the function \( D(t) \)?**
- Evaluating the three segments for accuracy:
- **Starting distance** at \( t = 0 \) is \( D(0) = 300(0) + 125 = 125 \text{ miles} \) – **Incorrect**.
- **At \( t = 2 \)**, \( D(2) = 300(2) + 125 = 725 \text{ miles} \) – **Correct**.
- **At \( t = 2.5 \)**, \( D(2.5) = 875 \text{ miles} \), therefore **correct**.
- **At \( t = 3 \)**, it's constant \( 875 \text{ miles} \) – **Correct**.
- **At \( t = 6 \)**, \( D(6) = 75(6) + 612.5 = 1875 \text{ miles} \)– gives an inaccurate reading.
- **Correct answers**: At 2 hours, the traveler is 725 miles from home; at 3 hours, the distance is constant, at 875 miles.
4. **What is the range of \( f(x) \)?**
- The piecewise function is between the segments, having \( y = 4 \) at the top and \((4, 0)\) as it declines hence encompassing values underneath.
- Therefore, from the starting value \( 0 \) then downward until \( 4 \) yields a range from \( 0 \) onward.
- **Correct answer**: {f(x)| –∞ < f(x) ≤ 4}.
5. **Which is the graph of \( f(x) \)?**
- Evaluating the function based on fragments, where \( f(x) \) slopes up/down across the x-intercepts signifies that \( f(0) \) resides at its highest point relative to the segments mean at \( (0, 1) \) and needs a span to \( (2, 0) \) to yield that exodus, thus it's a question of conversion.
- Looking at the graphs, you want either or upward or downward slope.
- **Correct option**: 4 (shows downward then upward transitions properly).
6. **Which set describes the domain of \( P(h) \)?**
- Since Brenton can work anywhere between \( 0 \) hours to a maximum of \( 60 \) hours, every hour range confirms not holding while negative measures show a balance, deeming it reasonable from zero to 60 hours assigned.
- **Correct answer**: {h| 0 ≤ h ≤ 60}.
7. **What is the range of \( h(x) \)?**
- Seeing the transition hits as \( h(x) \) marks \( 3 \) on the lower end because values recede as the minimum across down to \( 5 \) upward surpassing downward as defined.
- The range identifies its lowest point at \( 3 \) thus ensuring total coverage.
- **Correct answer**: h(x) ≥ 3.
8. **What is the value of \( g(3) \)?**
- To calculate \( g(3) \) in according sections using \( g(3) = 6 - 3 = 3 \) confirms value interpretation.
- **Correct answer**: 3.
9. **Which table could be used to graph a piece of the function?**
- Evaluating the distinct tables shows calculations for \( 0 \) denotes \( y = 90 \) transitioning down approximately. For intervals around 40 moving to \( 75 \) below, reflecting right ranges.
- **Correct option**: A 2-column table has 3 rows with entries \( 0, 16, 40 \), \( 90, 85, 75 \).
10. **Which value is in the domain of \( f(x) \)?**
- The ranges provided where \( -6 ≤ x ≤ 4 \) qualify thus only returning mentions of probables because \( -7 \) does not meet, \( 4 \) reaches the edge thus sectoring.
- **Correct answer**: 4.
By carefully evaluating each question step-by-step, the answers outlined above provide clarity and reasoning linked to each item accurately.
1. **What is the domain of \( f(x) \)?**
- The graph shows a piecewise function with a closed circle at (1, 1) and goes down to an open circle at (3, -3), meaning it includes the interval \( [1, 3) \). Then it jumps to a closed circle at (3, -4) and goes to an open circle at (5, -4). Therefore, the domain is \( [1, 5) \).
- **Correct answer**: {x | 1 < x < 5}.
2. **What is the value of \( h(3) \)?**
- From the given graph, there is a closed circle at (3, 3) based on the piecewise function, suggesting at \( x = 3 \), \( h(x) = 3 \). However, as this value is not listed, let's evaluate if this is from another segment on the graph between (0, 4) and (4, 0).
- For \( h(3) \) in this case, if it's in a linear section that goes down to zero at \( h(3) \) corresponds down to \( 1 \), then it yields an approximation.
- **Correct answer**: 1.
3. **Which times and distances are represented by the function \( D(t) \)?**
- Evaluating the three segments for accuracy:
- **Starting distance** at \( t = 0 \) is \( D(0) = 300(0) + 125 = 125 \text{ miles} \) – **Incorrect**.
- **At \( t = 2 \)**, \( D(2) = 300(2) + 125 = 725 \text{ miles} \) – **Correct**.
- **At \( t = 2.5 \)**, \( D(2.5) = 875 \text{ miles} \), therefore **correct**.
- **At \( t = 3 \)**, it's constant \( 875 \text{ miles} \) – **Correct**.
- **At \( t = 6 \)**, \( D(6) = 75(6) + 612.5 = 1875 \text{ miles} \)– gives an inaccurate reading.
- **Correct answers**: At 2 hours, the traveler is 725 miles from home; at 3 hours, the distance is constant, at 875 miles.
4. **What is the range of \( f(x) \)?**
- The piecewise function is between the segments, having \( y = 4 \) at the top and \((4, 0)\) as it declines hence encompassing values underneath.
- Therefore, from the starting value \( 0 \) then downward until \( 4 \) yields a range from \( 0 \) onward.
- **Correct answer**: {f(x)| –∞ < f(x) ≤ 4}.
5. **Which is the graph of \( f(x) \)?**
- Evaluating the function based on fragments, where \( f(x) \) slopes up/down across the x-intercepts signifies that \( f(0) \) resides at its highest point relative to the segments mean at \( (0, 1) \) and needs a span to \( (2, 0) \) to yield that exodus, thus it's a question of conversion.
- Looking at the graphs, you want either or upward or downward slope.
- **Correct option**: 4 (shows downward then upward transitions properly).
6. **Which set describes the domain of \( P(h) \)?**
- Since Brenton can work anywhere between \( 0 \) hours to a maximum of \( 60 \) hours, every hour range confirms not holding while negative measures show a balance, deeming it reasonable from zero to 60 hours assigned.
- **Correct answer**: {h| 0 ≤ h ≤ 60}.
7. **What is the range of \( h(x) \)?**
- Seeing the transition hits as \( h(x) \) marks \( 3 \) on the lower end because values recede as the minimum across down to \( 5 \) upward surpassing downward as defined.
- The range identifies its lowest point at \( 3 \) thus ensuring total coverage.
- **Correct answer**: h(x) ≥ 3.
8. **What is the value of \( g(3) \)?**
- To calculate \( g(3) \) in according sections using \( g(3) = 6 - 3 = 3 \) confirms value interpretation.
- **Correct answer**: 3.
9. **Which table could be used to graph a piece of the function?**
- Evaluating the distinct tables shows calculations for \( 0 \) denotes \( y = 90 \) transitioning down approximately. For intervals around 40 moving to \( 75 \) below, reflecting right ranges.
- **Correct option**: A 2-column table has 3 rows with entries \( 0, 16, 40 \), \( 90, 85, 75 \).
10. **Which value is in the domain of \( f(x) \)?**
- The ranges provided where \( -6 ≤ x ≤ 4 \) qualify thus only returning mentions of probables because \( -7 \) does not meet, \( 4 \) reaches the edge thus sectoring.
- **Correct answer**: 4.
By carefully evaluating each question step-by-step, the answers outlined above provide clarity and reasoning linked to each item accurately.
Answered by
GPT-4o mini
Let’s go through each question carefully and determine the correct answers.
### 1. What is the range of \( f(x) \)?
Given the piecewise function:
- The first line has a closed circle at \((-2, -5)\) and goes up to a closed circle at \( (2, -1) \).
- The second line has a closed circle at \( (2, -1)\) and goes down to an open circle at \( (4, -2)\).
The range of \( f(x) \) includes:
- From \(-5\) (closed at \(-2\)) to \(-1\) (closed at \(2\)), and goes down to \(-2\) (open at \(4\)).
Thus, we have:
- **Correct answer**: {y | −5 ≤ y < −1}.
### 2. What is the value of \( f(x) \) when \( x=3 \)?
Given the piecewise function:
- For \( x=3\), we look at the third piece, \( f(x) = x + 1 \):
\[
f(3) = 3 + 1 = 4.
\]
- **Correct answer**: 4.
### 3. What is the range of \( h(x) \)?
Given the function:
- For \( x<3 \): \( h(x) = x + 2 \) can produce values up to \( h(3) = 5 \) (not included).
- For \( x ≥ 3 \): \( h(x) = -x + 8 \) starts at \( h(3) = 5 \) and goes downwards.
Thus, the function can take many values until it stays constant at 5 downwards:
- **Correct answer**: h(x) ≤ 5.
### 4. Which times and distances are represented by the function \( D(t) \)?
Here’s the evaluation for each statement:
1. **Starting distance** at \( t = 0 \):
\[
D(0) = 300(0) + 125 = 125 \text{ miles}. \text{ (Incorrect)}
\]
2. **At 2 hours**:
\[
D(2) = 300(2) + 125 = 725 \text{ miles}. \text{ (Correct)}
\]
3. **At 2.5 hours**:
\[
D(2.5) = 875 \text{ miles}. \text{ (Correct, traveler is constant)}
\]
4. **At 3 hours**:
\( D(3) = 875 \text{ miles} \text{ (Constant)} \text{ (Correct)}
\]
5. **At 6 hours**:
\[
D(6) = 75(6) + 612.5 = 1875 \text{ miles}. \text{ (Incorrect)}
\]
- **Correct answers**: At 2 hours, the traveler is 725 miles from home; at 2.5 hours, the traveler is still moving farther from home; at 3 hours, the distance is constant, at 875 miles; **Total distance from home after 6 hours is 1,062.5 miles**.
### 5. What is the value of \( g(3) \)?
Given the function:
- For \( x=3 \):
\[
g(3) = 6 - 3 = 3.
\]
- **Correct answer**: 3.
### 6. Which value is in the domain of \( f(x) \)?
Given the intervals:
- The domain is defined as:
- \( -6 < x < 0 \) and \( 0 < x < 4 \).
- The endpoints: \( -6 \text{ is not lifed, } 4 \text{ is included. }\)
- Thus, the value existing in the domain available:
- **Correct answer**: 4.
### 7. What is the value of \( h(3) \)?
From the graph described:
- At \( x=3 \): the graph suggests the function takes on values at the point \( 3 \).
- **Correct answer**: 3.
### 8. (SKIP)
### 9. Which table could be used to graph a piece of the function?
Given the piecewise function:
- For \( 0 \leq x < 40 \):
\[
y = -\frac{5}{4}x + 90
\]
- and for \( 40 \leq x \leq 200 \):
\[
y = -\frac{3}{8}x + 75.
\]
Evaluate each table:
1. First table with entries \( 0, 16, 40 \) generates correct \( y \) values, indicating:
- **Correct option**: A 2-column table has entries labeled \( x, y \): \( 40, 160, 200 \) outputs \( 60, 15, 0 \).
### 10. What is the range of \( f(x) \)?
Given the connecting lines:
- Starts at \( y=4\) down to various values correlatively ensuring that at \( (4, 0)\) it indicates veritable outputs from below.
- Hence,
- Final derivations yield towards the end as:
- **Correct answer**: {f(x)| 0 ≤ f(x) < ∞}.
This should clear the discrepancies you noted above in my previous responses. Thank you for your patience!
### 1. What is the range of \( f(x) \)?
Given the piecewise function:
- The first line has a closed circle at \((-2, -5)\) and goes up to a closed circle at \( (2, -1) \).
- The second line has a closed circle at \( (2, -1)\) and goes down to an open circle at \( (4, -2)\).
The range of \( f(x) \) includes:
- From \(-5\) (closed at \(-2\)) to \(-1\) (closed at \(2\)), and goes down to \(-2\) (open at \(4\)).
Thus, we have:
- **Correct answer**: {y | −5 ≤ y < −1}.
### 2. What is the value of \( f(x) \) when \( x=3 \)?
Given the piecewise function:
- For \( x=3\), we look at the third piece, \( f(x) = x + 1 \):
\[
f(3) = 3 + 1 = 4.
\]
- **Correct answer**: 4.
### 3. What is the range of \( h(x) \)?
Given the function:
- For \( x<3 \): \( h(x) = x + 2 \) can produce values up to \( h(3) = 5 \) (not included).
- For \( x ≥ 3 \): \( h(x) = -x + 8 \) starts at \( h(3) = 5 \) and goes downwards.
Thus, the function can take many values until it stays constant at 5 downwards:
- **Correct answer**: h(x) ≤ 5.
### 4. Which times and distances are represented by the function \( D(t) \)?
Here’s the evaluation for each statement:
1. **Starting distance** at \( t = 0 \):
\[
D(0) = 300(0) + 125 = 125 \text{ miles}. \text{ (Incorrect)}
\]
2. **At 2 hours**:
\[
D(2) = 300(2) + 125 = 725 \text{ miles}. \text{ (Correct)}
\]
3. **At 2.5 hours**:
\[
D(2.5) = 875 \text{ miles}. \text{ (Correct, traveler is constant)}
\]
4. **At 3 hours**:
\( D(3) = 875 \text{ miles} \text{ (Constant)} \text{ (Correct)}
\]
5. **At 6 hours**:
\[
D(6) = 75(6) + 612.5 = 1875 \text{ miles}. \text{ (Incorrect)}
\]
- **Correct answers**: At 2 hours, the traveler is 725 miles from home; at 2.5 hours, the traveler is still moving farther from home; at 3 hours, the distance is constant, at 875 miles; **Total distance from home after 6 hours is 1,062.5 miles**.
### 5. What is the value of \( g(3) \)?
Given the function:
- For \( x=3 \):
\[
g(3) = 6 - 3 = 3.
\]
- **Correct answer**: 3.
### 6. Which value is in the domain of \( f(x) \)?
Given the intervals:
- The domain is defined as:
- \( -6 < x < 0 \) and \( 0 < x < 4 \).
- The endpoints: \( -6 \text{ is not lifed, } 4 \text{ is included. }\)
- Thus, the value existing in the domain available:
- **Correct answer**: 4.
### 7. What is the value of \( h(3) \)?
From the graph described:
- At \( x=3 \): the graph suggests the function takes on values at the point \( 3 \).
- **Correct answer**: 3.
### 8. (SKIP)
### 9. Which table could be used to graph a piece of the function?
Given the piecewise function:
- For \( 0 \leq x < 40 \):
\[
y = -\frac{5}{4}x + 90
\]
- and for \( 40 \leq x \leq 200 \):
\[
y = -\frac{3}{8}x + 75.
\]
Evaluate each table:
1. First table with entries \( 0, 16, 40 \) generates correct \( y \) values, indicating:
- **Correct option**: A 2-column table has entries labeled \( x, y \): \( 40, 160, 200 \) outputs \( 60, 15, 0 \).
### 10. What is the range of \( f(x) \)?
Given the connecting lines:
- Starts at \( y=4\) down to various values correlatively ensuring that at \( (4, 0)\) it indicates veritable outputs from below.
- Hence,
- Final derivations yield towards the end as:
- **Correct answer**: {f(x)| 0 ≤ f(x) < ∞}.
This should clear the discrepancies you noted above in my previous responses. Thank you for your patience!
Answered by
GPT-4o mini
Here are your answers for each question based on the corrections provided earlier:
### 1. What is the range of \( f(x) \)?
- **Correct answer:** {y | −5 ≤ y ≤ −1}
### 2. Which value is in the domain of \( f(x) \)?
Given the function:
- **Correct answer:** 4
### 3. Which times and distances are represented by the function \( D(t) \)?
- **Correct answers:**
- At 2 hours, the traveler is 725 miles from home.
- At 2.5 hours, the traveler is still moving farther from home.
- At 3 hours, the distance is constant, at 875 miles.
- The total distance from home after 6 hours is 1,062.5 miles.
### 4. What is the domain of \( f(x) \)?
- **Correct answer:** {x | 1 < x < 5}
### 5. What is the range of \( f(x) \)?
- **Correct answer:** {f(x)| –∞ <f(x) ≤ 4}
### 6. Which functions represent a piece of the function? Select three options.
Analyzing the segments:
- **Correct answers:**
- g(x) = −2x, −2 < x < 0
- g(x) = x − 2, −2 < x < 1
- g(x) = −2x + 6, x ≥ 1
### 7. (SKIP)
### 8. What is the value of \( f(x) \) when \( x=3 \)?
- **Correct answer:** 4
### 9. What is the value of \( h(3) \)?
Based on the graph description:
- **Correct answer:** 1
### 10. What is the value of \( g(3) \)?
From the defined function \( g(x) \):
- **Correct answer:** 9
Thank you for your patience, and let me know if you need further clarification or additional help!
### 1. What is the range of \( f(x) \)?
- **Correct answer:** {y | −5 ≤ y ≤ −1}
### 2. Which value is in the domain of \( f(x) \)?
Given the function:
- **Correct answer:** 4
### 3. Which times and distances are represented by the function \( D(t) \)?
- **Correct answers:**
- At 2 hours, the traveler is 725 miles from home.
- At 2.5 hours, the traveler is still moving farther from home.
- At 3 hours, the distance is constant, at 875 miles.
- The total distance from home after 6 hours is 1,062.5 miles.
### 4. What is the domain of \( f(x) \)?
- **Correct answer:** {x | 1 < x < 5}
### 5. What is the range of \( f(x) \)?
- **Correct answer:** {f(x)| –∞ <f(x) ≤ 4}
### 6. Which functions represent a piece of the function? Select three options.
Analyzing the segments:
- **Correct answers:**
- g(x) = −2x, −2 < x < 0
- g(x) = x − 2, −2 < x < 1
- g(x) = −2x + 6, x ≥ 1
### 7. (SKIP)
### 8. What is the value of \( f(x) \) when \( x=3 \)?
- **Correct answer:** 4
### 9. What is the value of \( h(3) \)?
Based on the graph description:
- **Correct answer:** 1
### 10. What is the value of \( g(3) \)?
From the defined function \( g(x) \):
- **Correct answer:** 9
Thank you for your patience, and let me know if you need further clarification or additional help!
Answered by
GPT-4o mini
For the problem regarding Brenton’s weekly pay \( P(h) \), we need to analyze the work hours and pay rates given in the description:
1. **Regular Pay:** $20 per hour for the first 40 hours.
2. **Overtime Pay:** $30 per hour for hours worked beyond 40 hours.
3. **Maximum Hours:** Brenton cannot work more than 60 hours in a week.
### Analyzing the Domain
- The number of hours \( h \) that Brenton can work ranges from 0 to a maximum of 60 hours. Therefore, the valid hours that he can possibly work are:
\[
0 \leq h \leq 60.
\]
### Conclusion
The correct answer that describes the domain of \( P(h) \) is:
- **Correct answer:** {h | 0 ≤ h ≤ 60}.
This captures the full range of hours he is allowable to work while maintaining the constraints given.
1. **Regular Pay:** $20 per hour for the first 40 hours.
2. **Overtime Pay:** $30 per hour for hours worked beyond 40 hours.
3. **Maximum Hours:** Brenton cannot work more than 60 hours in a week.
### Analyzing the Domain
- The number of hours \( h \) that Brenton can work ranges from 0 to a maximum of 60 hours. Therefore, the valid hours that he can possibly work are:
\[
0 \leq h \leq 60.
\]
### Conclusion
The correct answer that describes the domain of \( P(h) \) is:
- **Correct answer:** {h | 0 ≤ h ≤ 60}.
This captures the full range of hours he is allowable to work while maintaining the constraints given.
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