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