Quiz about PRECALCULUS -- AP EXAM REView

Question 1

Question 1.

Accepted Answer

16

Answer

-16

Answer

0

Answer

18

Question 2

Question 2.

Accepted Answer

400

Answer

200

Answer

1600

Answer

3200

Question 3

Question 3.

Accepted Answer

7/6

Answer

0

Answer

1/3

Answer

2

Question 4

Question 4.

Accepted Answer

Question 5

Which of the following best approximates the x-value at the inflection point for the polynomial y = f(x) graph above?

Accepted Answer

x = -1.5

Answer

x = -6.6

Answer

x = -4

Answer

x =3

Question 6

Question 6.

Accepted Answer

Question 7

Question 7.

Accepted Answer

6

Answer

2

Answer

4

Answer

5

Question 8

Question 8.

Accepted Answer

3/2

Answer

2/3

Answer

2

Answer

8

Question 9

Question 9.

Accepted Answer

II and III only

Answer

II only

Answer

I and II only

Answer

I, II, and III

Question 10

Question 10.

Accepted Answer

Question 11

Question 11.

Accepted Answer

I and II only

Answer

I only

Answer

II only

Answer

I, II, and III

Question 12

Ashley purchases a car and records its value over the next 4 years. Which of the following functions best models the value of the car t years after its purchase?

Accepted Answer

Question 13

Question 13.

Accepted Answer

III only

Answer

I only

Answer

I and II only

Answer

II and III only

Question 14

Question 14.

Accepted Answer

Question 15

Which of the following equations represents the graph above?

Accepted Answer

Question 16

Question 16.

Accepted Answer

Question 17

Question 17.

Accepted Answer

Question 18

If $$f\left(x\right)=2x$$ and $$g\left(x\right)=2x^2-1$$ find $$f\left(g\left(x\right)\right)$$

Accepted Answer

$$4x^2-2$$

Answer

$$4x^2-1$$

Answer

$$8x^2-1$$

Answer

$$16x^2-1$$

Question 19

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

Accepted Answer

reflects over x-axis, left 3, down 6

Answer

It stayed the same

Answer

reflects, up 3, left 6

Answer

reflects over y-axis, right 3, down 6

Question 20

Write the function for the following table:

Accepted Answer

$$f(x)=1(3)^x$$

Answer

$$f(x)=3(3)^x$$

Answer

$$f(x)=3x+3$$

Question 21

Find the inverse of $$f(x)=\frac{x-5}{3}$$

Accepted Answer

$$f^{-1}(x)=3x+5$$

Answer

$$f^{-1}(x)=\frac{3}{5}+x$$

Answer

$$f^{-1}(x)=5x+3$$

Question 22

Find the inverse of $$f(x)=\frac{x-5}{3}$$

Accepted Answer

$$f^{-1}(x)=3x+5$$

Answer

$$f^{-1}(x)=\frac{3}{5}+x$$

Answer

$$f^{-1}(x)=5x+3$$

Question 23

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

Accepted Answer

a_n = 7n - 17

Answer

a_n= 10n + 17

Answer

a_n = -7n + 17

Answer

a_n = 7n + 3

Question 24

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

Accepted Answer

Container C

Answer

Container A

Answer

Container B

Answer

Container D

Question 25

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

Accepted Answer

Container C

Answer

Container A

Answer

Container B

Answer

Container D

Question 26

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

Accepted Answer

Container C

Answer

Container A

Answer

Container B

Answer

Container D

Question 27

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and the total distance he has fallen, in feet, is the dependent variable?

Accepted Answer

Question 28

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and his distance from the ground, in feet, is the dependent variable?

Accepted Answer

Question 29

The figure shows a conical tank with water pouring into it. At t = 0, water begins to pour into the empty tank. The rate that water pours into the tank varies in such a way that the depth of the water inside the tank increases at a constant rate with respect to time. Which of the following graphs could depict this situation, where the depth of the water inside the tank, in feet, is the independent variable and the volume of water inside the tank, in cubic feet, is the dependent variable?

Accepted Answer

Question 30

Which of the following statements about the graph of f is correct for the interval 1 < x < 3?

Accepted Answer

(C) f is decreasing at an increasing rate.

Answer

(A) f is increasing at an increasing rate.

Answer

(B) f is increasing at a decreasing rate.

Answer

(D) f is decreasing at a decreasing rate.

Question 31

Which of the following statements about the graph of f is correct for the interval 0 < x < 1?

Accepted Answer

(D) f is decreasing and the graph of f is concave down.

Answer

(A) f is increasing and the graph of f is concave up.

Answer

(B) f is increasing and the graph of f is concave down.

Answer

(C) f is decreasing and the graph of f is concave up.

Question 32

Which of the following statements about the graph of f is correct for the interval 5 < x < 7?

Accepted Answer

(C) The rate of change of f is negative and increasing.

Answer

(A) The rate of change of f is positive and increasing.

Answer

(B) The rate of change of f is positive and decreasing.

Answer

(D) The rate of change of f is negative and decreasing.

Question 33

Use the graph of g below for this problem. How many points of inflection does the graph of g have?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 34

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

Accepted Answer

On the interval 0 < x < 2, g is positive and decreasing.

Answer

On the interval 0 < x < 2, g is positive and increasing.

Answer

On the interval 0 < x < 2, g is negative and increasing.

Answer

On the interval 0 < x < 2, g is negative and decreasing.

Question 35

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

Accepted Answer

On the interval 5 < x < 6, g is decreasing at a decreasing rate.

Answer

On the interval 5 < x < 6, g is increasing at an increasing rate.

Answer

On the interval 5 < x < 6, g is increasing at a decreasing rate.

Answer

On the interval 5 < x < 6, g is decreasing at an increasing rate.

Question 36

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

Accepted Answer

On the interval 4 < x < 5, g is increasing and the graph of g is concave down.

Answer

On the interval 4 < x < 5, g is increasing and the graph of g is concave up.

Answer

On the interval 4 < x < 5, g is decreasing and the graph of g is concave up.

Answer

On the interval 4 < x < 5, g is decreasing and the graph of g is concave down.

Question 37

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

Accepted Answer

On the interval 7 < x < 8, the rate of change of g is negative and increasing.

Answer

On the interval 7 < x < 8, the rate of change of g is positive and increasing.

Answer

On the interval 7 < x < 8, the rate of change of g is positive and decreasing.

Answer

On the interval 7 < x < 8, the rate of change of g is negative and decreasing.

Question 38

Over which of the following closed intervals is the average rate of change of f equal to 0? Use the graph of f below to answer.

Accepted Answer

[2, 5]

Answer

[0, 2]

Answer

[2, 4]

Answer

[2, 6]

Question 39

Over which of the following closed intervals is the average rate of change of f the least? Use the graph of f below to answer.

Accepted Answer

[5, 8]

Answer

[0, 4]

Answer

[0, 8]

Answer

[6, 8]

Question 40

What is the average rate of change of f over the closed interval from x = 2 to x = 6? Use the graph of f below to answer.

Accepted Answer

-3/4

Answer

-4/3

Answer

-1/2

Answer

1/2

Question 41

What is the average rate of change of f over the closed interval [4, 8]? Use the graph of f below to answer.

Accepted Answer

-1

Answer

-4

Answer

-2

Answer

1

Question 42

What is the average rate of change of f over the closed interval [3, 5]? Use the graph of f below to answer.

Accepted Answer

1/2

Answer

1

Answer

3/2

Answer

2

Question 43

Let k be the piecewise function defined by k(x) as given. Over the closed interval -4 <= x <= 2, the average rate of change of k is 2. What is the value of a?

Accepted Answer

13

Answer

1/27

Answer

1/13

Answer

27

Question 44

Let h be the piecewise function defined by h(x) as given. What is the average rate of change of h over the closed interval from x = 1 to x = 5?

Accepted Answer

-3

Answer

-13/4

Answer

-1/3

Answer

6

Question 45

Let g be the piecewise function defined by g(x) as given. What is the average rate of change of g over the closed interval [-2, 4]?

Accepted Answer

7/3

Answer

-2

Answer

1

Answer

2

Question 46

The table gives values for a continuous function h at selected values of x. What is the average rate of change of h over the closed interval [3, 9]?

Accepted Answer

-1/2

Answer

-2

Answer

-1

Answer

1/2

Question 47

The table gives values for a continuous function f at selected values of x. What is the average rate of change of f over the closed interval [0, 3]?

Accepted Answer

2

Answer

1/2

Answer

1

Answer

3

Question 48

The figure shows the graph of a function f in the xy-plane with four labeled points. It is known that a relative maximum of f occurs at D, and the only point of inflection of the graph of f is C. Of the following points, at which is the rate of change of f the greatest?

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 49

The figure shows the graph of a function j in the xy-plane with four labeled points. It is known that a relative minimum of j occurs at D, and the only point of inflection of the graph of j is C. Of the following points, at which is the rate of change of j the least?

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 50

The figure shows the graph of a function h in the xy-plane with four labeled points. It is known that a relative maximum of h occurs at C. For which of the following pairs of points is the average rate of change of h the least?

Accepted Answer

D) between points C and D

Answer

A) between points A and C

Answer

B) between points B and C

Answer

C) between points B and D

Question 51

The figure shows the graph of a function k in the xy-plane with three labeled points. It is known that a relative maximum of k occurs at B. Consider the rates of change of k at the three labeled points. Which of the following orders the rates of change of k in order from least to greatest?

Accepted Answer

D) C, B, A

Answer

A) A, B, C

Answer

B) B, A, C

Answer

C) C, A, B

Question 52

The figure shows the graph of a function k in the xy-plane with three labeled points. It is known that a relative maximum of k occurs at B. Consider the rates of change of k at the three labeled points. Which of the following orders the rates of change of k in order from least to greatest?

Accepted Answer

D) C, B, A

Answer

A) A, B, C

Answer

B) B, A, C

Answer

C) C, A, B

Question 53

Which of the following statements about the interval from E to F is true?

Accepted Answer

The graph of g is concave down, because the rate of change of g is decreasing.

Answer

The graph of g is concave up, because the rate of change of g is positive.

Answer

The graph of g is concave up, because the rate of change of g is increasing.

Answer

The graph of g is concave down, because the rate of change of g is negative.

Question 54

Which of the following statements about the interval from C to E is true?

Accepted Answer

The rate of change of g is increasing.

Answer

The graph of g is positive.

Answer

The graph of g is increasing.

Answer

The rate of change of g is positive.

Question 55

Which of the following statements about the interval from A to B is true?

Accepted Answer

The function g is increasing at a decreasing rate.

Answer

The function g is increasing at an increasing rate.

Answer

The function g is decreasing at an increasing rate.

Answer

The function g is decreasing at a decreasing rate.

Question 56

Use the graph of f shown in the diagram to answer this question. On which intervals is f decreasing at an increasing rate?

Accepted Answer

the interval from C to D

Answer

the interval from 4 to B

Answer

the interval from B to C

Answer

the interval from D to E

Question 57

Use the graph of f shown in the diagram to answer this question. On which intervals is the rate of change of f positive?

Accepted Answer

the intervals from 4 to B and from D to E

Answer

the interval from 4 to B only

Answer

the intervals from 4 to B and from B to C

Answer

the intervals from C to D and from D to E

Question 58

Use the graph of f shown in the diagram to answer this question. On which intervals is f increasing and the graph of f concave down?

Accepted Answer

the interval from A to B

Answer

the interval from B to C

Answer

the interval from C to D

Answer

the interval from D to E

Question 59

Use the graph of f shown in the diagram to answer this question. On which intervals is the rate of change of f increasing?

Accepted Answer

the intervals from C to D and from D to E

Answer

the interval from A to B only

Answer

the interval from D to E only

Answer

the intervals from A to B and from D to E

PRECALCULUS -- AP EXAM REView

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