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)