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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 \PageIndex{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 \PageIndex{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 \PageIndex{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 \PageIndex{4}

f(x)=5x−2

Answer

a. −2 b. 3 c. 13 d. −5x−2 e. 5a−2 f. 5a+5h−2

Exercise \PageIndex{5}

f(x)=\frac{2}{x}

Answer

a. Undefined b. 2 c. 23 d. −\frac{2}{x} e \frac{2}{a} f. \frac{2}{a+h}

Exercise \PageIndex{6}

f(x)=\sqrt{6x+5}

Answer

a. \sqrt{5} b. \sqrt{11} c. \sqrt{23} d. \sqrt{−6x+5} e. \sqrt{6a+5} f. \sqrt{6a+6h+5}

Exercise \PageIndex{7}

f(x)=|x−7|+8

Answer

a. 15 b. 14 c. 12 d. |x+7|+8 e. |a−7|+8 f. |a+h−7|+8

Exercise \PageIndex{8}

f(x)=\frac{x−2}{3x+7}

Answer

a. \frac{-2}{7} b. -.1 c. \frac{1}{17} d. -\frac{x+2}{-3x+7} e \frac{a−2}{3a+7} f. \frac{a+h−2}{3a+3h+7}

Exercise \PageIndex{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 \PageIndex{10}

g(x)=\sqrt{8x−1}

Answer

x≥\frac{1}{8};y≥0;x=\frac{1}{8}; no y-intercept

Exercise \PageIndex{11}

f(x)=−1+\sqrt{x+2}

Answer

x≥−2;y≥−1;x=−1;y=−1+\sqrt{2}

Exercise \PageIndex{12}

g(x)=\frac{3}{x−4}

Answer

x≠4;y≠0; no x-intercept; y=−\frac{3}{4}

Exercise \PageIndex{13}

g(x)=\sqrt{\frac{7}{x−5}}

Answer

x>5;y>0; no intercepts

Exercise \PageIndex{14}

f(x)=\frac{x}{x^2−16}

Answer

x≠\pm 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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