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# 1. Find the area of the region determined by the inequalities

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1. Find the area of the region determined by the inequalities $$y \ge |x| and y \leq -|x+1| + 4.$$

2. For an integer n let $$f(n) = \left\{ \begin{array}{cl} \frac{n}{2} & \text{if n is even}, \\ 3n + 1 & \text{if n is odd}. \end{array} \right. Find f(f(f(f(12)))).$$

3. Find the area of the region that lies below the graph of $$y = 3 - |x - 1|$$  but above the -axis.

.4.Let  $$f(x) = \left\{ \begin{array}{cl} -2x & \text{if } x < 0, \\ \frac{x}{2} & \text{if } x \ge 0. \end{array} \right.$$ Find the range of  Enter your answer in interval notation.

5. Let $$f(x) = \left\{ \begin{array}{cl} 3x & \text{if } x < 3, \\ 3^x & \text{if } x \ge 3. \end{array} \right. Find f(2) + f(3) + f(4).$$

May 6, 2021

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1. The area is 18.

2. f(f(f(f(f(12)))) = 14.

3. The area is 20.

4. The range is [-16,4).

5. f(2) + f(3) + f(4) = 28.

May 6, 2021
#2
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Sorry these are all incorrect

Guest May 6, 2021