Question

given the piecewise defined function:$f(x)=\begin{cases}-2x - 5 & \text{if } x leq -3 \\x + 5 & \text{if } x > -3end{cases}$draw the graph of $f$. note: be sure to include closed or open dots, but only at breaks in the graph.clear all draw:

Explanation:

Step1: Find point for $x\leq-3$

Substitute $x=-3$ into $f(x)=-2x-5$:
$f(-3)=-2(-3)-5=6-5=1$
This is a closed dot at $(-3,1)$ since $x\leq-3$ includes $x=-3$.

Step2: Find second point for $x\leq-3$

Choose $x=-4$:
$f(-4)=-2(-4)-5=8-5=3$
Plot $(-4,3)$, draw line through $(-3,1)$ and $(-4,3)$, extending left.

Step3: Find point for $x>-3$

Substitute $x=-3$ into $f(x)=x+5$:
$f(-3)=-3+5=2$
This is an open dot at $(-3,2)$ since $x>-3$ excludes $x=-3$.

Step4: Find second point for $x>-3$

Choose $x=0$:
$f(0)=0+5=5$
Plot $(0,5)$, draw line through $(-3,2)$ (open dot) and $(0,5)$, extending right.

Answer:

• For $x\leq-3$: A line passing through $(-3, 1)$ (closed dot) and $(-4, 3)$, extending leftward.
• For $x>-3$: A line passing through $(-3, 2)$ (open dot) and $(0, 5)$, extending rightward.