1.2E: Domain and Range

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SECTION 1.2 EXERCISE

Write the domain and range of the function using interval notation.

1. $屏幕快照 2019-06-06 下午1.55.29.png$ 2. $屏幕快照 2019-06-06 下午1.56.03.png$

Write the domain and range of each graph as an inequality.

3. $屏幕快照 2019-06-06 下午1.56.25.png$ 4. $屏幕快照 2019-06-06 下午1.56.56.png$

Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time, stopping once the sub surfaces. What is the domain and range of the function in the graph?

5. $屏幕快照 2019-06-06 下午1.57.31.png$ 6. $屏幕快照 2019-06-06 下午1.57.56.png$

Find the domain of each function

$7. f\left(x\right)=3\sqrt{x-2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8. f\left(x\right)=5\sqrt{x+3}$

$9. f\left(x\right)=3-\sqrt{6-2x}\ \ \ \ \ \ \ \ \ \ \ 10. f\left(x\right)=5-\sqrt{10-2x}$

$11. f\left(x\right)=\dfrac{9}{x\; -\; 6}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12. f\left(x\right)=\dfrac{6}{x\; -\; 8}$

$13. f\left(x\right)=\dfrac{3x+1}{4x+2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 14. f\left(x\right)=\dfrac{5x+3}{4x-1}$

$15. f\left(x\right)=\dfrac{\sqrt{x+4} }{x-4}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 16. f\left(x\right)=\dfrac{\sqrt{x+5} }{x-6}$

$17. f\left(x\right)=\dfrac{x\; -3}{x^{2} +\; 9x\; -22}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 18. f\left(x\right)=\dfrac{x\; -8}{x^{2} +\; 8x\; -9}$

Given each function, evaluate: $f(-1)$, $f(0)$, $f(2)$, $f(4)$

$19. f\left(x\right)=\left\{\begin{array}{ccc} {7x+3} & {if} & {x<0} \\ {7x+6} & {if} & {x\ge 0} \end{array}\right.\ \ \ \ \ \ \ \ \ \ \ \ \ \ 20. f\left(x\right)=\left\{\begin{array}{ccc} {4x-9} & {if} & {x<0} \\ {4x-18} & {if} & {x\ge 0} \end{array}\right.$

$21. f\left(x\right)=\left\{\begin{array}{ccc} {x^{2} -2} & {if} & {x<2} \\ {4+\left|x-5\right|} & {if} & {x\ge 2} \end{array}\right.\ \ \ \ \ \ 22. f\left(x\right)=\left\{\begin{array}{ccc} {4-x^{3} } & {if} & {x<1} \\ {\sqrt{x+1} } & {if} & {x\ge 1} \end{array}\right.$

$23. f\left(x\right)=\left\{\begin{array}{ccc} {5x} & {if} & {x<0} \\ {3} & {if} & {0\le x\le 3} \\ {x^{2} } & {if} & {x>3} \end{array}\right.\ \ \ \ \ \ \ \ \ \ \ \ \ \ 24. f\left(x\right)=\left\{\begin{array}{ccc} {x^{3} +1} & {if} & {x<0} \\ {4} & {if} & {0\le x\le 3} \\ {3x+1} & {if} & {x>3} \end{array}\right.$

Write a formula for the piecewise function graphed below.

25. $屏幕快照 2019-06-06 下午2.05.45.png$ 26. $屏幕快照 2019-06-06 下午2.06.21.png$

27. $屏幕快照 2019-06-06 下午2.06.48.png$ 28. $屏幕快照 2019-06-06 下午2.07.22.png$

29. $屏幕快照 2019-06-06 下午2.07.51.png$ 30. $屏幕快照 2019-06-06 下午2.08.25.png$

Sketch a graph of each piecewise function

$31. f\left(x\right)=\left\{\begin{array}{ccc} {\left|x\right|} & {if} & {x<2} \\ {5} & {if} & {x\ge 2} \end{array}\right.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 32. f\left(x\right)=\left\{\begin{array}{ccc} {4} & {if} & {x<0} \\ {\sqrt{x} } & {if} & {x\ge 0} \end{array}\right.$

$33. f\left(x\right)=\left\{\begin{array}{ccc} {x^{2} } & {if} & {x<0} \\ {x+2} & {if} & {x\ge 0} \end{array}\right.\ \ \ \ \ \ \ \ \ \ \ \ \ \ 34. f\left(x\right)=\left\{\begin{array}{ccc} {x+1} & {if} & {x<1} \\ {x^{3} } & {if} & {x\ge 1} \end{array}\right.$

$35. f\left(x\right)=\left\{\begin{array}{ccc} {3} & {if} & {x\le -2} \\ {-x+1} & {if} & {-2<x\le 1} \\ {3} & {if} & {x>1} \end{array}\right.\ \ \ \ \ \ \ \ 36. f\left(x\right)=\left\{\begin{array}{ccc} {-3} & {if} & {x\le -2} \\ {x-1} & {if} & {-2<x\le 2} \\ {0} & {if} & {x>2} \end{array}\right.$

Answer

1. D: [-5, 3) R: [0, 2]

3. D: $2< t \le 8$ R: $6 \le g(t) < 8$

5. D: [0, 4] R: [-3, 0]

7. $[2, \infty)$

9. $-\infty, 3]$

11. $(\infty, 6) \cup (6, \infty)$

13. $(-\infty, -\dfrac{1}{2}) \cup (-\dfrac{1}{2}, \infty)$

15. $[-4, 4) \cup (4, \infty)$

17. $(-\infty, -11) \cup (-11, 2) \cup (2, \infty)$

	$f(-1)$	$f(0)$	$f(2)$	$f(4)$
19.	-4	6	20	34
21.	-1	-2	7	5
23.	-5	3	3	16

25. $f(x) = \begin{cases} 2 & if & -6 \le x \le -1 \\ -2 & if & -1 < x \le 2 \\ -4 & if & 2 < x \le 4 \end{cases}$

27. $f(x) = \begin{cases} 3 & if & x \le 0 \\ x^2 & if & x > 0 \end{cases}$

29. $f(x) = \begin{cases} \dfrac{1}{x} & if & x < 0 \\ \sqrt{x} & if & x \ge 0 \end{cases}$

31. $Screen Shot 2019-08-20 at 10.51.31 AM.png$ 33. $Screen Shot 2019-08-20 at 10.53.00 AM.png$

35. $Screen Shot 2019-08-20 at 10.54.08 AM.png$

	\(f(-1)\)	\(f(0)\)	\(f(2)\)	\(f(4)\)
19.	-4	6	20	34
21.	-1	-2	7	5
23.	-5	3	3	16