Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Precalculus 2e

Practice Test

Precalculus 2ePractice Test

Practice Test

For the following exercises, determine whether each of the following relations is a function.

1.

y=2x+8 y=2x+8

2.

{ (2,1),(3,2),(−1,1),(0,−2) } { (2,1),(3,2),(−1,1),(0,−2) }

For the following exercises, evaluate the function f(x)=−3 x 2 +2x f(x)=−3 x 2 +2x at the given input.

3.

f(−2) f(−2)

4.

f(a) f(a)

5.

Show that the function f(x)=−2 (x−1) 2 +3 f(x)=−2 (x−1) 2 +3 is not one-to-one.

6.

Write the domain of the function f(x)= 3−x f(x)= 3−x in interval notation.

7.

Given f(x)=2 x 2 −5x, f(x)=2 x 2 −5x, find f(a+1)−f(1). f(a+1)−f(1).

8.

Graph the function f(x)={ x+1   if −2<x<3    −x    if   x≥3 f(x)={ x+1   if −2<x<3    −x    if   x≥3

9.

Find the average rate of change of the function f(x)=3−2 x 2 +x f(x)=3−2 x 2 +x by finding f(b)−f(a) b−a . f(b)−f(a) b−a .

For the following exercises, use the functions f(x)=3−2 x 2 +x and g(x)= x f(x)=3−2 x 2 +x and g(x)= x to find the composite functions.

10.

( g∘f )(x) ( g∘f )(x)

11.

( g∘f )(1) ( g∘f )(1)

12.

Express H(x)= 5 x 2 −3x 3 H(x)= 5 x 2 −3x 3 as a composition of two functions, f f and g, g, where ( f∘g )(x)=H(x). ( f∘g )(x)=H(x).

For the following exercises, graph the functions by translating, stretching, and/or compressing a toolkit function.

13.

f(x)= x+6 −1 f(x)= x+6 −1

14.

f(x)= 1 x+2 −1 f(x)= 1 x+2 −1

For the following exercises, determine whether the functions are even, odd, or neither.

15.

f(x)=− 5 x 2 +9 x 6 f(x)=− 5 x 2 +9 x 6

16.

f(x)=− 5 x 3 +9 x 5 f(x)=− 5 x 3 +9 x 5

17.

f(x)= 1 x f(x)= 1 x

18.

Graph the absolute value function f(x)=−2| x−1 |+3. f(x)=−2| x−1 |+3.

19.

Solve | 2x−3 |=17. | 2x−3 |=17.

20.

Solve −| 1 3 x−3 |≥17. −| 1 3 x−3 |≥17. Express the solution in interval notation.

For the following exercises, find the inverse of the function.

21.

f(x)=3x−5 f(x)=3x−5

22.

f(x)= 4 x+7 f(x)= 4 x+7

For the following exercises, use the graph of g g shown in Figure 1.

Graph of a cubic function.
Figure 1
23.

On what intervals is the function increasing?

24.

On what intervals is the function decreasing?

25.

Approximate the local minimum of the function. Express the answer as an ordered pair. The ordered pair should include both the xx value as well as the g(x)g(x) value.

26.

Approximate the local maximum of the function. Express the answer as an ordered pair. The ordered pair should include both the xx value as well as the g(x)g(x) value.

For the following exercises, use the graph of the piecewise function shown in Figure 2.

Graph of absolute function and step function.
Figure 2
27.

Find f(2). f(2).

28.

Find f(−2). f(−2).

29.

Write an equation for the piecewise function.

For the following exercises, use the values listed in Table 1.

x x 0 1 2 3 4 5 6 7 8
f(x) f(x) 1 3 5 7 9 11 13 15 17
Table 1
30.

Find f(6). f(6).

31.

Solve the equation f(x)=5. f(x)=5.

32.

Is the graph increasing or decreasing on its domain?

33.

Is the function represented by the graph one-to-one?

34.

Find f −1 (15). f −1 (15).

35.

Given f(x)=−2x+11, f(x)=−2x+11, find f −1 (x). f −1 (x).

PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/precalculus-2e/pages/1-introduction-to-functions
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/precalculus-2e/pages/1-introduction-to-functions
Citation information

© Jun 28, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.