2.0E: Exercises
This page is a draft and is under active development.
( \newcommand{\kernel}{\mathrm{null}\,}\)
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)=5x−2
- Answer
-
a. −2 b. 3 c. 13 d. −5x−2 e. 5a−2 f. 5a+5h−2
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)=|x−7|+8
- Answer
-
a. 15 b. 14 c. 12 d. |x+7|+8 e. |a−7|+8 f. |a+h−7|+8
Exercise 2.0.8
f(x)=x−23x+7
- Answer
-
a. \frac{-2}{7} b. −.1 c. 117 d. −x+2−3x+7 e a−23a+7 f. a+h−23a+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)=√8x−1
- Answer
-
x≥18;y≥0;x=18; no y-intercept
Exercise 2.0.11
f(x)=−1+√x+2
- Answer
-
x≥−2;y≥−1;x=−1;y=−1+√2
Exercise 2.0.12
g(x)=3x−4
- Answer
-
x≠4;y≠0; no x-intercept; y=−34
Exercise 2.0.13
g(x)=√7x−5
- Answer
-
x>5;y>0; no intercepts
Exercise 2.0.14
f(x)=xx2−16
- 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)