Question

graph the piece - wise function given below.
f(x)=\begin{cases}-x&\text{for }-3 < x < 4\\|x - 5|+4&\text{for }4 < x < 7end{cases}
step 1: select a function then move with blue dot (if necessary)

Explanation:

Step1: Analyze $y = -x$ for $- 3

This is a linear - function with slope $m=-1$ and $y$ - intercept $b = 0$. When $x=-3$, $y = 3$; when $x = 4$, $y=-4$. We draw a straight - line segment between the points $(-3,3)$ and $(4, - 4)$ (open - circles at the endpoints since the inequality is strict).

Step2: Analyze $y=\vert x - 5\vert+4$ for $4

The parent function of $y=\vert x\vert$ is a V - shaped function. The function $y=\vert x - 5\vert+4$ is a translation of $y = \vert x\vert$ 5 units to the right and 4 units up.
When $x = 4$, $y=\vert4 - 5\vert+4=\vert-1\vert+4=5$.
When $x = 7$, $y=\vert7 - 5\vert+4=\vert2\vert+4=6$.
We draw the V - shaped part of the function $y=\vert x - 5\vert+4$ for the domain $4

Answer:

Graph a line segment $y=-x$ for $-3