College Algebra, Chapter 3, 3.1, Section 3.1, Problem 30

Evaluate the piecewise defined function $f(x) = \left\{
\begin{array}{c}
3x & \text{if} & x < 0 \\
x+1 & \text{if} & 0 \leq x \leq 2\\
(x-2)^2 & \text{if} & x > 2
\end{array}\right.
\quad
$
at $f(-5), f(0), f(1), f(2), f(5)$



$
\begin{equation}
\begin{aligned}
&\text{Since } -5 \leq 2, \text{ we have } f(-5) = 3(-5) = -15\\
\\
&\text{Since } 0 \leq 0 \leq 2, \text{ we have } f(0) = 0+1 = 1\\
\\
&\text{Since } 0 \leq 1 \leq 2, \text{ we have } f(1) = 1 + 1 = 2\\
\\
&\text{Since } 0 \leq 2 \leq 2, \text{ we have } f(2) = 2 + 1 = 3\\
\\
&\text{Since } 5 > 2, \text{ we have } f(5) = (5-2)^2 = 3^2 = 9\\
\\
\end{aligned}
\end{equation}
$