1. The graph of y = 4 – StartRoot 2 x EndRoot is shown.
On a coordinate plane, a curved line approaches the grid line at (3, 1.5) and ends at (0, 4).
Which statement about the graph is accurate?
The x-intercept of the graph is (4, 0).
The graph has no y-intercepts.
The maximum of the graph occurs at the y-intercept.
The minimum of the graph occurs at the x-intercept.
2. A 2-column table with 4 rows. The first column is labeled x with entries negative 6, negative 1, 0, 3. The second column is labeled y with entries negative 7, 1, 9, negative 2.
What is the domain of the given function?
{x | x = –6, –1, 0, 3}
{y | y = –7, –2, 1, 9}
{x | x = –7, –6, –2, –1, 0, 1, 3, 9}
{y | y = –7, –6, –2, –1, 0, 1, 3, 9}
3. A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
4. On a coordinate plane, a curved line with a minimum value of (0, 1) and a maximum value of (negative 1.3, 2.2), crosses the x-axis at (negative 2.2, 0) and crosses the y-axis at (0, 1).
Which statement correctly identifies a local minimum of the graphed function?
Over the interval [–3, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 2.2.
Over the interval [–1, 0.5], the local minimum is 1.
Over the interval [0.5, 2], the local minimum is 4.
5. A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 0, 2, 8, 2, 0, negative 2.
What are all of the x-intercepts of the continuous function in the table?
6. On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0).
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to –3
7. The graph of the function f(x) is shown below.
On a coordinate plane, a curved line with a minimum value of (0.6, 2.5) and a maximum value of (negative 1.2, 18.3), crosses the x-axis at (negative 1.8, 0) and crosses the y-axis at (0, 5).
What is x when f(x)=0?
-1.8
-1.2
0
5
8. A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?
9. Graph the function y = |1.6x – 2| – 3.2. Over which interval is the function increasing?
(1.25, ∞)
(3.25, ∞)
(–∞, 1.25)
(–∞, 3.25)
10. Which best describes the relationship between the successive terms in the sequence shown?
2.4, –4.8, 9.6, –19.2
The common difference is –7.2.
The common difference is –2.4.
The common ratio is –2.0.
The common ratio is –0.5.
7 answers
Here are the answers to your questions:
Which statement about the graph is accurate?
The maximum of the graph occurs at the y-intercept.
What is the domain of the given function?
{x | x = –6, –1, 0, 3}
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
Which statement correctly identifies a local minimum of the graphed function?
Over the interval [–1, 0.5], the local minimum is 1.
What are all of the x-intercepts of the continuous function in the table?
(–4, 0), (4, 0)
What is the range of the function on the graph?
All the real numbers greater than or equal to –3.
What is x when f(x)=0?
-1.8
Which sequence could be generated using the formula?
–12, –18, –27, ...
Over which interval is the function increasing?
(1.25, ∞)
Which best describes the relationship between the successive terms in the sequence shown?
The common ratio is –2.0.
If you have any further questions or need clarification on any of the answers, feel free to ask!
11. Consider the function represented by the table.
What is f(0)?
4
5
6
7
12. The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.
What does h(3.2) represent?
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
13. Analyze the graphed function to find the local minimum and the local maximum for the given function.
On a coordinate plane, a curved line with minimum values of (0.6, negative 8) and (3.4, negative 8), and a maximum value of (2, 0), crosses the x-axis at (0, 0), (2, 0), and (4, 0), and crosses the y-axis at (0, 0).
Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
14. The graph represents a functional relationship.
On a coordinate plane, a straight line with a negative slope begins at point (1, 3), crosses the x-axis at (4, 0), and exits the plane at (18, negative 14).
Which value is an input of the function?
–14
–2
0
4
15. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, negative 3, negative 3, 4, 1, 3.
What ordered pair is closest to a local minimum of the function, f(x)?
(–1, –3)
(0, –2)
(1, 4)
(2, 1)
16. Which is the graph of y = –|2x + 1|?
On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 0.5, negative 3) and (2.5, negative 3) and has a vertex of (1, 0). It crosses the y-axis at (0, negative 2).
On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 2.5, negative 3) and (0.5, negative 3) and has a vertex of (negative 1, 0). It crosses the y-axis at (0, negative 2).
On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 2, negative 3) and (2, negative 3) and has a vertex of (0, 1). It crosses the x-axis at (negative 0.5, 0) and (0.5, 0).
On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 2, negative 3) and (1, negative 3) and has a vertex of (negative 0.5, 0). It crosses the y-axis at (0, negative 1).
17. Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?
18. A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 15, negative 5, 0, 5, 0, negative 5.
Which is a valid prediction about the continuous function f(x)?
f(x) ≤ 0 over the interval (–∞, ∞).
f(x) > 0 over the interval (–1, ∞).
f(x) ≥ 0 over the interval [–1, 1].
f(x) < 0 over the interval (0, 2).
19. For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function C of F = five-ninths (F minus 32) . What does C(F) represent?
the temperature of F degrees Fahrenheit converted to degrees Celsius
the temperature of F degrees Celsius converted to degrees Fahrenheit
the temperature of C degrees Fahrenheit converted to degrees Celsius
the temperature of C degrees Celsius converted to degrees Fahrenheit
20. Which graph shows a set of ordered pairs that represent a function?
On a coordinate plane, solid circles appear at the following points: (negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5).
On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
Here are the answers to your new questions:
What is f(0)?
4
What does h(3.2) represent?
The height of the rock 3.2 seconds after it is propelled.
Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Which value is an input of the function?
4
What ordered pair is closest to a local minimum of the function, f(x)?
(0, –3)
Which is the graph of y = –|2x + 1|?
On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 2.5, negative 3) and (0.5, negative 3) and has a vertex of (negative 1, 0). It crosses the y-axis at (0, negative 2).
Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?
f(n + 1) = (–0.5)f(n)
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [–1, 1].
What does C(F) represent?
The temperature of F degrees Fahrenheit converted to degrees Celsius.
Which graph shows a set of ordered pairs that represent a function?
On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4). (This set includes the point (4, -3) and (4, 4), which are two distinct y-values for the same x-value, so it does not represent a function. The right answer would be for a set where no x value corresponds to more than one y value.)
Feel free to ask for further clarification or if you have any other questions!
for 20 and 16 say the graph as in its 1,2,3,4.
and for 15. THERE IS NO 0,-3?? (–1, –3)
(0, –2)
(1, 4)
(2, 1)
21. Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....
Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.
Which best explains which student is correct?
Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –2.
Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5.
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
22. The table represents a function.
A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12.
Which value is an output of the function?
–6
–2
4
7
23. Which equation is graphed below?
On a coordinate plane, a hyperbola has a curve in quadrant 2 and a curve in quadrant 4. The curve in quadrant 2 enters the grid line at (negative 3, 1) and (negative 0.5, 6). The curve in quadrant 4 enters the plane at (0. 5, negative 6) and (3, negative 1).
y = –StartFraction 3 Over x EndFraction
y = StartFraction 2 over x EndFraction
y = –2square root of x
y = 3square root of x
24. Which set of ordered pairs represents a function?
25. The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V and five-sevenths represent?
the radius of the rubber ball when the volume equals five-sevenths cubic feet
the volume of the rubber ball when the radius equals five-sevenths feet
that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
Here are the updated answers, including the corrections and responses to your new questions:
Updated Previous Answers:
What ordered pair is closest to a local minimum of the function, f(x)?
(–1, –3) (You are correct; this value does appear in your table).
Which is the graph of y = –|2x + 1|?
Graph 2. (On a coordinate plane, an angled line opens down. It approaches the grid line at (negative 2.5, negative 3) and (0.5, negative 3) and has a vertex of (negative 1, 0). It crosses the y-axis at (0, negative 2).)
Which graph shows a set of ordered pairs that represent a function?
Graph 2. (On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4). This is because the point (4, 4) and (4, -3) violates the function rule, so no graph contains a valid set of points to represent a function. The correct answer is a graph that does not contain duplicate x-values with different y-values.)
New Questions:
Which best explains which student is correct?
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways. (Taquan's sequence does indeed multiply by -2, but Julia's prediction does not fit the arithmetic definition with a common difference.)
Which value is an output of the function?
–2 (This value appears as a corresponding output in the function.)
Which equation is graphed below?
y = –StartFraction 3 Over x EndFraction (The description suggests a hyperbola that opens downwards as described in quadrants II and IV).
Which set of ordered pairs represents a function?
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} (In this set, every x-value is unique, meaning it qualifies as a function.)
What does V and five-sevenths represent?
The volume of the rubber ball when the radius equals five-sevenths feet.
If you have more questions or need further clarification, please let me know!
76.. Well i passed at least and its not like i know anything about math so good enough!
Congratulations on passing! That's a great achievement, especially if math isn't your strong suit. Remember, every bit of progress counts, and learning takes time. If you need help with any specific concepts in the future or just want to practice, feel free to reach out. Keep up the great work, and don’t hesitate to keep learning! 🎉📚
