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Mathematics LibreTexts

2.0E: Exercises

This page is a draft and is under active development. 

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For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

Exercise 2.0.1

x y x y
-3 9 1 1
-2 4 2 4
-1 1 3 9
0 0
Answer

a. Domain = {3,2,1,0,1,2,3}, range = {0,1,4,9}

b. Yes, a function

Exercise 2.0.2

x y x y
1 -3 1 1
2 -2 2 2
3 -1 3 3
0 0
Answer

a. Domain = {0,1,2,3}, range = {3,2,1,0,1,2,3}

b. No, not a function

Exercise 2.0.3

x y x y
3 3 15 1
5 2 21 2
8 1 33 3
10 0
Answer

a. Domain = {3,5,8,10,15,21,33}, range = {0,1,2,3}

b. Yes, a function

For the following exercises, find the values for each function, if they exist, then simplify.

a. f(0) b. f(1) c. f(3) d. f(x) e. f(a) f. f(a+h)

Exercise 2.0.4

f(x)=5x2

Answer

a. 2 b. 3 c. 13 d. 5x2 e. 5a2 f. 5a+5h2

Exercise 2.0.5

f(x)=2x

Answer

a. Undefined b. 2 c. 23 d. 2x e 2a f. 2a+h

Exercise 2.0.6

f(x)=6x+5

Answer

a. 5 b. 11 c. 23 d. 6x+5 e. 6a+5 f. 6a+6h+5

Exercise 2.0.7

f(x)=|x7|+8

Answer

a. 15 b. 14 c. 12 d. |x+7|+8 e. |a7|+8 f. |a+h7|+8

Exercise 2.0.8

f(x)=x23x+7

Answer

a. \frac{-2}{7} b. .1 c. 117 d. x+23x+7 e a23a+7 f. a+h23a+3h+7

Exercise 2.0.9

f(x)=9

Answer

a. 9 b. 9 c. 9 d. 9 e. 9 f. 9

For the following exercises, find the domain, range, and all zeros/intercepts, if any, of the functions.

Exercise 2.0.10

g(x)=8x1

Answer

x18;y0;x=18; no y-intercept

Exercise 2.0.11

f(x)=1+x+2

Answer

x2;y1;x=1;y=1+2

Exercise 2.0.12

g(x)=3x4

Answer

x4;y0; no x-intercept; y=34

Exercise 2.0.13

g(x)=7x5

Answer

x>5;y>0; no intercepts

Exercise 2.0.14

f(x)=xx216

Answer

x±4; x=0,y=0

Contributors and Attributions

Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.

Pamini Thangarajah (Mount Royal University, Calgary, Alberta, Canada)


2.0E: Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

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