The function $f$ is defined as $$f( x) =\left\{ \begin{array}{c@{\qquad}l} 0 & \hbox{if }x \lt 0 \\ 10 & \hbox{if }0\leq x\leq 100 \\ 0.2x-10 & \hbox{if }x \gt 100 \end{array} \right.$$

Figure 11

Solution (a) $f( -1) =0;$ $f( 100) =10;$ $f( 200) =0.2( 200) -10=30$

(b) The graph of $f$ consists of three pieces corresponding to each equation in the definition. The graph is the horizontal line $y= 0$ on the interval $( -\infty ,0) ,$ the horizontal line $y=10$ on the interval $[ 0,100]$, and the line $y=0.2x-10$ on the interval $( 100,\infty )$, as shown in Figure 11.

(c) $f$ is a piecewise-defined function. Look at the values that $x$ can take on: $x<0,$ $0\leq x\leq 100,$ $x>100.$ We conclude the domain of $f$ is all real numbers. The range of $f$ is the number $0$ and all real numbers greater than or equal to $10.$ The $x$-intercepts are all the numbers in the interval $( -\infty ,0)$; the $y$-intercept is $10$.