1.0E Exercises
- Page ID
- 10622
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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
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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
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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
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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
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\(x≥\frac{1}{8};y≥0;x=\frac{1}{8}\); 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
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\(x≠4;y≠0\); no x-intercept; \(y=−\frac{3}{4}\)
Exercise \(\PageIndex{13}\)
\(g(x)=\sqrt{\frac{7}{x−5}}\)
- Answer
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\(x>5;y>0\); no intercepts
Exercise \(\PageIndex{14}\)
\(f(x)=\frac{x}{x^2−16}\)
- Answer
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\(x≠\pm 4\); \(x=0,y=0\)
Contributors
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)