Free Printable AP Precalculus - Unit 2 Review

1.

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A

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d)

D

2.

Calculator OK.

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C

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D

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a)

A

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B

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C

d)

D

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C

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D

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Calculator OK.

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C

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D

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C

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D

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C

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D

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A

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C

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D

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A

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B

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C

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D

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C

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a)

A

b)

B

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C

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D

14.

a)

A

b)

B

c)

C

d)

D

15.

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

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

16.

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

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects over y-axis, right 3, down 6

d)

reflects over x-axis, left 3, down 6

17.

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

a)

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

b)

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

c)

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

18.

Write the EXPLICIT rule for the arithmetic sequence

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

a)

a_n= 10n + 17

b)

a_n = 7n - 17

c)

a_n = -7n + 17

d)

a_n = 7n + 3

19.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

20.

Which of the following is an equivalent form of $y=6\cdot4^x$ ?

a)

$y=6\cdot2^{3x}$

b)

$y=6\cdot2^{\frac{x}{2}}$

c)

$y=6\cdot16^{\left(\frac{x}{2}\right)}$

d)

$y=3\cdot2^{2x}$

21.

As x values increase without bound, what are the y-values approaching in the function $y=2\cdot3^{-x}$ ?

a)

∞

b)

-∞

c)

0

d)

2

22.

Find g(f(-2))

a)

-18

b)

-2

c)

1

d)

9

23.

For the function $f(x) = \sqrt{x-4}$ , find $f^{-1}(x)$ .

a)

$f^{-1}(x) = x^2 + 4$

b)

$f^{-1}(x) = (x + 4)^2$

c)

$f^{-1}(x) = x^2 - 4$

d)

$f^{-1}(x) = (x^2) + 4$

24.

Which of the following statements is true about the exponential function $g$ given by $g(x) = \frac{1}{2} \cdot 3^x$ ?

a)

g is always increasing, and the graph of g is always concave up.

b)

g is always increasing, and the graph of g is always concave down.

c)

g is always decreasing, and the graph of g is always concave up.

d)

g is always decreasing, and the graph of g is always concave down.

25.

Which of the following statements is true about the exponential function $f$ given by $f(x) = 7 \left( \frac{4}{5} \right)^x$ ?

a)

(A) $f$ is increasing at an increasing rate.

b)

(B) $f$ is increasing at a decreasing rate.

c)

(C) $f$ is decreasing at an increasing rate.

d)

(D) $f$ is decreasing at a decreasing rate.

26.

The figure shows a portion of the graph of a function h. Which of the following conclusions is possible for h?

a)

h is logarithmic because the output values are proportional over equal-length input-value intervals.

b)

h is logarithmic because the output values are proportional over equal-length output-value intervals.

c)

h is exponential because the output values are proportional over equal-length input-value intervals.

d)

h is exponential because the output values are proportional over equal-length output-value intervals.

27.

The function f is given by f(x) = 36 · 4^x. Which of the following is an equivalent form for f(x)?

a)

f(x) = $6 · 2^{2x}$

b)

f(x) = $6 · 2^{2x}$

c)

f(x) = $36 · 2^{x/2}$

d)

f(x) = $36 · 2^{2x}$

28.

The function $j$ is given by $j(x)=3\cdot4^{(x+2)}$ . Which of the following is an equivalent form for $j(x)$ ?

a)

j(x) = $48^x$

b)

j(x) = $48 \cdot 4^x$

c)

j(x) = $3 \cdot 16^x$

d)

$j(x) = 9 \cdot 16^x$

29.

Which of the following functions is an equivalent form of the function g(x) = $3 \cdot 5^{2x}$ ?

a)

g(x) = $75^x$

b)

g(x) = $3 \cdot 25^x$

c)

g(x) = $9 · 5^x$

d)

g(x) = $9 · 25^x$

30.

The function $h$ is given by $h(x) = 25 \cdot 16^{(x/2)}$ . Which of the following is an equivalent form for $h(x)$ ?

a)

$h(x) = 100^x$

b)

$h(x) = 5 \cdot 4^x$

c)

$h(x) = 25 \cdot 4^x$

d)

$h(x) = 25 \cdot 8^x$

31.

In the xy-plane, the function f, given by f(x) = $4^{(x-2)}$ , is a horizontal translation of the exponential function g, given by g(x) = $4^x$ . Which of the following is an equivalent form for f(x) that expresses f as a vertical dilation of g?

a)

f(x) = $-2 · 4^x$

b)

f(x) = $16 · 4^x$

c)

f(x) = $\frac{1}{16} \cdot 4^x$

d)

f(x) = $1/4 · 4^x$

32.

The graph of a function f is a horizontal dilation of y = $3^x$ , and f(x) is equivalent to $(\sqrt{3})^x$ . Which of the following could be an expression for f(x)?

a)

$3^{x/2}$

b)

$3^{2x}$

c)

$9^{x/2}$

d)

$g^{2(x)}$

33.

The increasing function C gives the number of cars that are stuck in traffic due to lane closures. The table gives values of C(t) for selected values of t, in minutes, since the beginning of the lane closures. If a model is constructed to represent these data, which of the following best applies to this situation?

a)

y = 30t + 10

b)

y = 300t + 10

c)

y = 10 $(\frac{1}{3})^t$

d)

$y = 10(3)^t$

34.

The table gives values for the functions f and g at selected values of x. Functions f and g are defined for all real numbers. Let h be the function defined by h(x) = g(f(x)). What is the value of h(9)?

a)

4

b)

7

c)

8

d)

10

35.

The graphs of f and g are shown for 0 ≤ x ≤ 9, each consisting of three line segments. Let h be the function defined by h(x) = g(f(x)). What is the value of h(8)?

a)

-2

b)

-1

c)

0

d)

2

36.

The function f is given by f(x) = $4^x$ , and the function g is given by g(x) = $3x$ . Which of the following is an expression for g(f(x))?

a)

$4^{3x}$

b)

$4^{6x}$

c)

$4^{9x}$

d)

$3 \cdot 4^x$

37.

The function f is given by f(x) = $2x - 1$ , and the function g is given by g(x) = $x^2 + 3x$ . Which of the following is an expression for g(f(x))?

a)

$2x^2 + 6x - 1$

b)

$4x^2 - x - 1$

c)

$4x^2 + 2x - 2$

d)

$2x^2 + 5x - 3x$

38.

The graph of the piecewise defined function h is shown above and consists of two line segments. The function k is the inverse of h, that is k = $h^{-1}$ . What is the minimum value of k?

a)

-4

b)

-3

c)

5

d)

2

39.

The graph of the piecewise defined function f is shown above and consists of three line segments. What is the value of $f^{-1}(3)$ ?

a)

-4

b)

-2

c)

2

d)

4

40.

The composition of any function, f(x), and
its inverse, f^-1(x) =

a)

x

b)

f(x)

c)

1

d)

0

41.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

42.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

43.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

44.

Are the following inverses of each other?

a)

True

b)

False

45.

Was the inverse function found correctly?

a)

no

b)

yes

46.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

47.

Are the blue and red graphs inverse functions?

a)

yes

b)

no

c)

no way to tell

48.

If f(x) = 3x-9, what is f^-1(12)?

a)

25

b)

9

c)

11

d)

7

49.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

50.

TRUE or FALSE
If f is an invertible function and f(a) = b, then f^-1(b) = a.

a)

TRUE

b)

FALSE

51.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

AP Precalculus - Unit 2 Review - Part 1

Total questions: 51

Worksheet time: 1hrs 17mins

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