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# 1.0E Exercises

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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

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

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

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 $$\PageIndex{4}$$

$$f(x)=5x−2$$

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

Exercise $$\PageIndex{5}$$

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

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

Exercise $$\PageIndex{6}$$

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

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

Exercise $$\PageIndex{7}$$

$$f(x)=|x−7|+8$$

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

Exercise $$\PageIndex{8}$$

$$f(x)=\frac{x−2}{3x+7}$$

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 $$\PageIndex{9}$$

$$f(x)=9$$

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 $$\PageIndex{10}$$

$$g(x)=\sqrt{8x−1}$$

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

Exercise $$\PageIndex{11}$$

$$f(x)=−1+\sqrt{x+2}$$

$$x≥−2;y≥−1;x=−1;y=−1+\sqrt{2}$$

Exercise $$\PageIndex{12}$$

$$g(x)=\frac{3}{x−4}$$

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

Exercise $$\PageIndex{13}$$

$$g(x)=\sqrt{\frac{7}{x−5}}$$

$$x>5;y>0$$; no intercepts

Exercise $$\PageIndex{14}$$

$$f(x)=\frac{x}{x^2−16}$$

$$x≠\pm 4$$; $$x=0,y=0$$