Answer
See graph
Work Step by Step
We are given the function:
$g(x)=\begin{cases}
x+6,x\leq -4\\
\dfrac{1}{2}x-4,x\gt 4
\end{cases}$
The function consists of two functions:
- the line $x+6$ defined on $(-\infty,-4]$
- the line $\dfrac{1}{2}x-4$ defined on $(-4,\infty)$
Graph the two functions:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/fb66feec-bfb6-49fc-a2a0-5f254ad8f4fb/steps_image/small_1586728597.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001922Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2dd77b7a33899b3a9ba8212e7cae07945c5af9a42b42756511b2317d17a01ad7)