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1.2E: Domain and Range

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    145521
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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.png30.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.png33. Screen Shot 2019-08-20 at 10.53.00 AM.png

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


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