Free Printable Big Review! AP Precalculus

1.

What does the average rate of change in a function represent?

a)

The function's concavity

b)

The function's symmetry

c)

The slope of the function

d)

The end behavior of the function

2.

When is a function considered positive?

a)

When its y values are below the x-axis

b)

When its y values are above the x-axis

c)

When its y values are getting smaller

d)

When its y values are getting larger

3.

What is the point of inflection on a graph?

a)

Where the slope of the function is zero

b)

Where the function is neither increasing nor decreasing

c)

Where the concavity of the function changes

d)

Where the function crosses the x-axis

4.

The given graph models Mr. Passwater’s distance from his home over time. Time, in hours, is the independent variable and the distance from home, in miles, is the dependent variable. Which of the following verbal descriptions would be appropriate for the given graph?

a)

Mr. Passwater leaves school and drives toward his house at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat dinner. After eating dinner, Mr. Passwater leaves and drives until he reaches his house, driving at a constant rate that is faster than the rate he was driving when he first left school.

b)

Mr. Passwater leaves school and drives toward his house, increasing his speed as he drives. Then, he drives at a constant rate for a period of time. Finally, he increases his speed again and drives until he reaches his home.

c)

Mr. Passwater leaves his house and drives at a constant rate to a nearby restaurant. After stopping for a period of time to eat lunch, Mr. Passwater drives back to his home at a constant rate that is faster than his rate when driving to the restaurant.

d)

Mr. Passwater leaves his house and drives to a restaurant at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat breakfast. After eating breakfast, Mr. Passwater leaves and drives until he reaches his school, driving at a constant rate that is faster than the rate he was driving when he first left his house.

5.

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

a)

1

b)

2

c)

3

d)

4

6.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

7.

At which following point does the graph of f(x) appear to be transitioning from concave down to concave up?

a)

B

b)

E

c)

G

d)

H

8.

Over which interval is the graph of f(x) both decreasing and concave up?

a)

(B, C)

b)

(D, E)

c)

(C, D)

d)

(H, I)

9.

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

10.

Over what intervals is the average rate of change decreasing?

a)

(-∞, 1)

b)

(0, 2)

c)

(-1, ∞)

d)

(-∞, 2)

11.

The slope can also be called...

a)

the function

b)

the rate of change

c)

increasing

d)

positive

12.

Let s(x) give the total snowfall, in inches, x hours from the start of the snowstorm. Which expression can be used to find the average rate at which snow fell between 2 and 5 hours after the start of the snowstorm?

a)

$\frac{s\left(5\right)\ -\ s\left(2\right)}{3}$

b)

$\frac{s\left(5\right)\ +\ s\left(2\right)}{3}$

c)

$\frac{s\left(2\right)\ -\ s\left(5\right)}{3}$

d)

$\frac{s\left(2\right)\ +\ s\left(5\right)}{3}$

13.

The graph of a function y = g(x) is shown. On which of the following intervals of x is g increasing at a decreasing rate?

a)

(-3, 1) U (4, ∞)

b)

(-1.4, 1) only

c)

(-1.4, 2.7)

d)

(-1.4, 1) U (4, ∞)

14.

Assuming the scale is 1, where is f(x) > 0?

a)

[-4, -1] U [2, +oo)

b)

(-4, -1) U (2, +oo)

c)

(-oo, -4] U [-1, 2]

d)

(-oo, -4) U (-1, 2)

15.

1.Let $k\left(x\right)=\frac{3x^2-4x+12}{x+2}$ . Which of the following statements about the graph of k is correct?

a)

The graph of k has a horizontal asymptote of y = 3.

b)

The graph of k has a slant asymptote of

y = 3x + 2.

c)

The graph of k has a slant asymptote of

y = 3x - 6.

d)

The graph of k has a slant asymptote

y = 3x - 10.

16.

2.The function g is a polynomial with the following end behavior:

$\lim_{x\rightarrow-\infty}g\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}g\left(x\right)=-\infty$

Which of the following could be an expression for g(x)?

a)

$-4x^7-3x^3+x-6$

b)

$-3x^6+5x^2+6x-1$

c)

$3x^3+x^2-5x+1$

d)

$2x^4-7x^3+3x^2+1$

17.

6.Selected values of a polynomial function $f$ are shown above. Let $g(x)=af(x+h)+k$ , where $a,h$ and $k$ are constants. In the xy-plane, the graph of $g$ is constructed by applying three transformations to the graph of $f$ in this order: a horizontal translation by $-3$ units, a vertical dilation by a factor of 2, and a vertical translation by 4 units. What is the value of $g\left(2\right)$ ?

a)

2

b)

12

c)

14

d)

16

18.

7.The polynomial function $f$ is given by $f(x)=(x+3)^4$ . Find the coefficient of the term containing $x^3$ .

a)

1

b)

12

c)

54

d)

81

19.

11.The function g is given by $g(x)=\frac{x^3+8x^2+12x}{x^2+2x-24}$ . What is the domain of g?

a)

all real numbers x where x ≠ 6, x ≠ 4

b)

all real numbers x where x ≠ 0, x ≠ -2

c)

all real numbers x where x ≠ 6, x ≠ 0, x ≠ -2

d)

all real numbers x where x ≠ 6, x ≠ 0, x ≠ -2, x ≠ 4

20.

12.The graph of the polynomial function $p$ is shown above. Which of the following could be an expression for $p$ ?

a)

$-\frac{1}{4}x(x+2)(x-3)$

b)

$-\frac{1}{4}x^2(x-2)(x+3)$

c)

$-\frac{1}{4}x^2(x+2)(x-3)$

d)

$\frac{1}{4}x^2(x+2)(x-3)$

21.

13.The function $f$ is given by $f(x)=x^2(x+3)(x^2+7)$ . Which of the following describes the zeros of $f$ ?

a)

f has exactly three distinct real zeros.

b)

f has exactly seven distinct real zeros.

c)

f has exactly two distinct real zeros and two non-real zeros.

d)

f has exactly three distinct real zeros and two non-real zeros.

22.

14.Determine the least possible degree of $g$ . Show the work that leads to your answer.

a)

0

b)

1

c)

2

d)

3

23.

If $f\left(x\right)=\frac{8x^3-8}{4x^3-2}$ , find the value of the following limit.

a)

2

b)

4

c)

8

d)

+∞

24.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

25.

The graph of the piecewise defined function f is shown above and consists of two line segments. The function g is the inverse of f, that is $g=f^{-1}$ . Which of the following is the graph of g, the inverse of f?

a)

b)

c)

d)

26.

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

a)

[-5, 4]

b)

[-4, 5]

c)

[-2, 3]

d)

[-1/4, 5]

27.

The table gives values of the increasing function f for selected values of x. What is the value of $f^{-1}\left(4\right)$ ?

a)

-5

b)

-2

c)

3

d)

6

28.

What is the value of $f^{-1}\left(g\left(4\right)\right)$ ?

a)

A) 2

b)

B) 3

c)

C) 5

d)

D) 7

29.

What is the value of $g^{-1}\left(f\left(2\right)\right)$ ?

a)

A) 2

b)

B) 4

c)

C) 5

d)

D) 7

30.

The function g is given by $g\left(x\right)=\log_3\left(x-4\right)$ . Which of the following statements about the construction of the inverse of g is true?

a)

The inverse of g cannot be constructed because the graph of g is not defined for all real values of x.

b)

The inverse of g can be constructed, and the graph of $g^{-1}$ has domain of all real values of x.

c)

The inverse of g can be constructed, and the graph of $g^{-1}$ has domain x > 4.

d)

The inverse of g can be constructed, and the graph of $g^{-1}$ has range of real values of y.

31.

The function f is given by $f\left(x\right)=\log_8x$ . What is the value of f(2)?

a)

-3

b)

1/4

c)

1/3

d)

3

32.

Let g be the logarithmic function given by $g\left(x\right)=-2\log_3x$ . Which of the following statements about g is true?

a)

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

b)

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

c)

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

d)

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

33.

Let k be the logarithmic function given by $k\left(x\right)=\frac{1}{4}\log_{10}x$ . Which of the following limit statements about the graph of k is true?

a)

$\lim_{x\rightarrow\infty}k\left(x\right)=0$

b)

$\lim_{x\rightarrow\infty}k\left(x\right)=\infty$

c)

$\lim_{x\rightarrow\infty}k\left(x\right)=-\infty$

d)

$\lim_{x\rightarrow0^+}k\left(x\right)=\infty$

34.

Let g be the logarithmic function given by $g\left(x\right)=3\log_2x$ . Which of the following statements about the end behavior of g is true?

a)

As the input values of g increase without bound, the output values decrease without bound.

b)

As the input values of g increase without bound, the output values get arbitrarily close to 0.

c)

As the input values of g decrease arbitrarily close to 0, the output values decrease without bound.

d)

As the input values of g decrease arbitrarily close to 0, the output values increase without bound.

35.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

36.

What does this graph represent?

a)

Exponential Decay

b)

Exponential Growth

37.

What is the initial value of the situation represented by f(x)=0.05(2)^x?

a)

0.05

b)

2

c)

0.1

d)

1

38.

a)

A

b)

B

c)

C

d)

D

39.

Any expression raised to the zero power is always equal to

a)

0

b)

1

c)

itself

d)

negative

40.

According to exponent rules, when we raise an exponential expression to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

41.

Simplify the expression $\frac{1}{w^{-5}}$

a)

$\frac{1}{w^5}$

b)

$w^5$

c)

$w^{-5}$

d)

$\frac{1}{w^{-5}}$

42.

$3^{5x}=243$ Solve for x

a)

x=1

b)

x=5

c)

x=1/5

d)

x=3

43.

$\ln\left(x-2\right)=3$ solve for x

a)

$x=e^3+2$

b)

$x=e^3-2$

c)

$x=e$

d)

$x=e^2+3$

44.

What is the correct transformed equation for the graph?

a)

y = log(x - 4)

b)

y = log(x) - 4

c)

y = log(x + 4)

d)

y = log(x) + 4

45.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

46.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

47.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

48.

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)

$16x^2-1$

49.

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

50.

Write the function for the following table:

a)

f(x)=1(3)^x

b)

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

c)

$f(x)=3x+3$

51.

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)

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

52.

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

53.

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

54.

Find g(f(-2))

a)

-18

b)

-2

c)

1

d)

9

55.

Factor: x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Not Factorable /(Prime)

56.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

57.

Factor
k²+7k+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

58.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Not Factorable (Prime)

59.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

Big Review! AP Precalculus

Total questions: 59

Worksheet time: 4hrs 35mins

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