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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
 #1
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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

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