# Piecewise-Defined Functions

1. Find the following, given that $y = \begin{cases} \sqrt{4-x^2}, & x \le 0\\ -3, & 0 \lt x \le 4\\ 2x-9, & x \gt 4 \end{cases}$

1. the domain   $\ans{\displaystyle{[-2,\infty)}}$

2. the range   $\ans{\displaystyle{\{-3\} \cup (-1,\infty)}}$

3. the graph of this function   $\ians{}$

2. Find the following, given that $y = \begin{cases} \sqrt{25-x^2}, & x \le 0\\ 2x+1, & 0 \lt x \lt 3\\ -4, & x \ge 3 \end{cases}$

1. the domain   $\ans{\displaystyle{[-5,\infty)}}$

2. the range   $\ans{\displaystyle{\{-4\} \cup [0,7)}}$

3. the graph of this function   $\ians{}$

3. Graph each of the following piece-wise defined functions and indicate the domain and range:

1. $\displaystyle{f(x) = \begin{cases} 3, & x \le -3\\ \left| x \right|, & -3 \lt x \le 3\\ -3, & x \gt 3 \end{cases}}$   $\ians{}$

2. $\displaystyle{f(x) = \begin{cases} \sqrt{x+1}, & x \lt 3\\ -2x+8, & x \ge 3 \end{cases}}$   $\ians{}$

3. $\displaystyle{f(x) = \begin{cases} \sqrt{4-x^2}, & x \le 0\\ -\sqrt{x+4}, & 0 \lt x \le 5 \end{cases}}$   $\ians{}$

4. $\displaystyle{f(x) = \begin{cases} -x-1, & x \le -4\\ 3, & -4 \lt x \lt 2\\ -x+5, & x \ge 2 \end{cases}}$   $\ians{}$