Question

1. graph the following piece - wise function: $f(x)=\begin{cases}\frac{1}{3}x + 4, & - 6leq xlt0\\5, & 0lt xleq3\\-2x + 8, & 3lt xlt6end{cases}$

Explanation:

Step1: Analyze first - piece function

For $y = \frac{1}{3}x + 4$ when $-6\leq x<0$. Find two points. When $x=-6$, $y=\frac{1}{3}\times(-6)+4=-2 + 4=2$. When $x = 0$, $y=\frac{1}{3}\times0+4 = 4$ (but $x = 0$ is not included, so use an open - circle at $(0,4)$ and a closed - circle at $(-6,2)$).

Step2: Analyze second - piece function

For $y = 5$ when $0

Step3: Analyze third - piece function

For $y=-2x + 8$ when $3eq3$). When $x = 6$, $y=-2\times6+8=-4$ (open - circle since $x
eq6$).

Answer:

To graph the piece - wise function, plot the points and lines as described above for each interval with the appropriate open and closed circles for the endpoints of the intervals.