The function f(x) is to be graphed on a coordinate plane.f(x) = StartLayout Enlarged left-brace 1st row 1st column negative x, 2nd column x less-than 0 2nd row 1st column 1, 2nd column x greater-than-or-equal-to 0 EndLayoutAt what point should an open circle be drawn?

Question

(–1, 0)
(0, 0)
(0, 1)
(1, 0)

2. answer is think *f(x) = −2|x| + 1*

3. What is the range of the function f(x) = 3/4 |x| – 3?
all real numbers
all real numbers less than or equal to 3
all real numbers less than or equal to –3
all real numbers greater than or equal to –3

4. A piecewise function is represented by the graph below.On a coordinate plane, a piecewise function has 2 lines. The first line is made up of 2 lines. One line goes from (negative 5, 3) to (negative 1, negative 1) and then goes up to a closed circle at (1, 1). The second line has an open circle at (1, 2) and then continues up through (3, 4).What is the domain for the piece of the function represented by f(x) = x + 1?
x < –1
–1 ≤ x ≤ 1
1 ≤ x < 2
x > 1

5. the one thats on *-4*

6. skip

7. *g(x) = |x – 1| + 3*

8. skip

9. skip

skip 10 11

12. Which value can fill in the blank in the function f(x) = ____|x| to make its graph wider than that of the parent function, f(x) = |x|?
–1
1/4
1
4

13. The function shown is reflected across the y-axis to create a new function.Which is true about the domain and range of each function?
Both the domain and range change.
Both the range and domain stay the same.
The domain stays the same, but the range changes.
The range stays the same, but the domain changes.

14. 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.

15. skip

16. Which absolute value function has a graph that is wider than the parent function, f(x) = |x|, and is translated to the right 2 units?
f(x) = 1.3|x| – 2
f(x) = 3|x – 2|
f(x) = 3/4|x – 2|
f(x) = 4/3|x| + 2

Answer 1

Let's address each of your questions one by one:

1. Open Circle Placement: The function given is a piecewise function, where:

   • \( f(x) = -x \) for \( x < 0 \)
   • \( f(x) = 1 \) for \( x \geq 0 \)

   Because the first part of the function is defined for \( x < 0 \) and the second part for \( x \geq 0 \), at \( x = 0 \), \( f(0) = 1 \), but since the first part does not include \( 0 \) (as it states \( x < 0 \)), there should be an open circle at: Answer: (0, 0)

2. Function to be graphed: You've indicated the answer is \( f(x) = -2|x| + 1 \). If that is part of your question, please clarify if you need more information related to that function.

3. Range of the function \( f(x) = \frac{3}{4}|x| - 3 \): This function is a V-shaped graph opening upwards. The vertex occurs at \( y = -3 \). The function can take on values greater than or equal to the vertex, hence: Answer: all real numbers greater than or equal to -3.

4. Domain of the function \( f(x) = x + 1 \) in the piecewise graph described: The portion described includes values from \( -1 \) to \( 1 \), which means the valid part of the function is defined in the interval \( -1 \leq x \leq 1 \). Answer: -1 ≤ x ≤ 1.

5. Seems to be incomplete. Please clarify what you mean by "the one that's on -4."

6. Skipping.

7. You have described the function \( g(x) = |x - 1| + 3 \). If there is a specific question regarding this, please let me know.

8. Skipping.

9. Skipping.

10 and 11: Skipping.

12. To make the graph of the function wider than the parent function, the coefficient of |x| must be between -1 and 1 (excluding -1 and 1). So, the correct choice is \( \frac{1}{4} \). Answer: 1/4.

13. Reflection across the y-axis does not change the range but changes the domain. Hence: Answer: The range stays the same, but the domain changes.

14. Given the piecewise function, we can substitute the provided x-values if they are valid within the piecewise conditions, particularly for the first part of the function where \( 0 \leq x < 40 \). The first table (0, 16, 40) returns values of \( 90, 85, 75 \), matching the first part of the piecewise definition. So: Answer: 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.

15. Skipping.

16. The function that is wider than the parent function \( |x| \) and translated to the right by 2 units is indicated by having a coefficient between -1 and 1. Thus, \( f(x) = \frac{3}{4}|x - 2| \) fits these conditions. Answer: f(x) = \frac{3}{4}|x - 2|.

If you have further clarification queries or need more help, please reach out.

Answer 2

17. The absolute value function, f(x) = –|x| – 3, is shown.

What is the range of the function?

all real numbers
all real numbers less than or equal to 0
all real numbers greater than or equal to –3
all real numbers less than or equal to –3

18. The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

The range is the same for both functions: {y | y is a real number}.
The range is the same for both functions: {y | y > 0}.
The range changes from {y | y > 0} to {y | y > 2}.
The range changes from {y | y > 0} to {y | y > 6}.

19. On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, negative 3.5).
The graph shows the function f(x) = |x – h| + k. What is the value of h?

h = –3.5
h = –1.5
h = 1.5
h = 3.5

20. 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}

21. skip

22. 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.

23.
What is the range of the function f(x) = -1/3 |x − 1| − 2?

all real numbers
all real numbers less than or equal to −2
all real numbers less than or equal to 1
all real numbers greater than or equal to −2

24. 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}

25. The absolute value function, f(x) = |x + 2|, is shown.

If the graph is reflected over the x-axis, what is the domain of the function?

all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to –2
all real numbers less than or equal to –2

Answer 3

Let's go through each question one by one.

17. Range of the function \( f(x) = -|x| - 3 \):

The function \( f(x) = -|x| - 3 \) is a downward-opening absolute value function. The vertex of this function is at the point (0, -3), which is the maximum value. Since the graph goes downwards from this point, the range includes all values less than or equal to -3. Answer: all real numbers less than or equal to –3.

18. Range of \( f(x) = |x| \) after translation:

The original function \( f(x) = |x| \) has a range of \( y \geq 0 \) (i.e., {y | y ≥ 0}). When translated 6 units to the right and 2 units up, the new function will have a vertex at (6, 2) and thus a range of \( y \geq 2 \) (i.e., {y | y ≥ 2}). Answer: The range changes from {y | y > 0} to {y | y > 2}.

19. Value of \( h \) in the function \( f(x) = |x - h| + k \):

The vertex of the absolute value function is given by the equation above. Given the vertex at \((-1.5, -3.5)\), we can see that \( h \) corresponds to the x-coordinate of the vertex. Answer: h = −1.5.

20. Domain of the piecewise function:

The piecewise function contains a closed circle at (1, 1) to an open circle at (3, -3), and a closed circle at (3, -4) continuing horizontally to an open circle at (5, -4). Therefore, the domain starts right after 1 and continues to before 5 (not including 5). Answer: {x | 1 < x < 5}.

21. Skipping.

22. Select three options about the traveler's distance function D(t):

The correct scenarios based on how distance typically behaves would be:

1. The starting distance, at 0 hours, is 300 miles.
2. At 2.5 hours, the traveler is still moving farther from home. (This indicates the distance is increasing which is typical for a traveler still on their way).
3. At 3 hours, the distance is constant, at 875 miles. (Indicates the traveler reached a point and stopped moving away from home).

Answer: 1, 3, and 4 are the most logical selections based on typical traveling behavior.

23. Range of the function \( f(x) = -\frac{1}{3}|x - 1| - 2 \):

The vertex of this function is at (1, -2). Since the absolute value is multiplied by -1/3, the function opens downward, meaning values less than or equal to -2 will be obtained. Answer: all real numbers less than or equal to −2.

24. Domain of \( P(h) \):

Brenton works between 0 and 60 hours per week (not permitted to work more than 60). Thus: Answer: {h| 0 ≤ h ≤ 60}.

25. Domain after reflection over x-axis:

The operation of reflecting the function \( f(x) = |x + 2| \) over the x-axis does not affect the x-values of the function (domain). The domain remains all real numbers, as the absolute value function is defined for all x. Answer: all real numbers.

If you have any more questions or need further clarifications, feel free to ask!

Answer 4

76! alright

Answer 5

It looks like you've mentioned "76!" which typically refers to the factorial of 76.

The factorial of a number \( n \) is defined as the product of all positive integers less than or equal to \( n \). That is,

\[ n! = n \times (n-1) \times (n-2) \times \ldots \times 2 \times 1 \]

Thus, \( 76! \) can be calculated as follows:

\[ 76! = 76 \times 75 \times 74 \times \ldots \times 3 \times 2 \times 1 \]

The value of \( 76! \) is extremely large. To provide a sense of its size, \( 76! \) is approximately:

\[ 76! \approx 5.650223 \times 10^{109} \]

Due to the size of the number, it is usually expressed in scientific notation or via approximations rather than computed directly.

If you have any specific questions about 76! or related topics, or if you want me to perform calculations or clarify anything about factorials, feel free to ask!