Question

graph this function.
f(x)=\begin{cases}\frac{2}{3}x + 3&\text{if }-6 < x < -3\\-x&\text{if }-3leq xleq4end{cases}
select points on the graph to plot them. select \point fill\ to change a point from closed to open.

Explanation:

Step1: For $y = \frac{2}{3}x + 3$, when $x=-6$, $y=\frac{2}{3}\times(-6)+3=-4 + 3=-1$ (not included as $x>-6$). When $x = - 3$, $y=\frac{2}{3}\times(-3)+3=-2 + 3 = 1$ (not included as $x<-3$).

Step2: For $y=-x$, when $x=-3$, $y=-(-3)=3$ (included). When $x = 4$, $y=-4$ (included).

Answer:

Plot points based on above - open circle at $(-6,-1)$, open circle at $(-3,1)$, closed circle at $(-3,3)$, closed circle at $(4,-4)$ and draw line segments for each part of the piece - wise function.