Question

graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}-4 & \\text{for } \\ x < -5 \\\\ 4x - 15 & \\text{for } \\ x > 3\\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Explanation:

Step1: Graph first piece: $f(x)=-4$

This is a horizontal line at $y=-4$, valid for $x < -5$. We draw a line from $(-10, -4)$ to an open circle at $(-5, -4)$ (open because $x=-5$ is not included).

Step2: Graph second piece: $f(x)=4x-15$

First, find the endpoint at $x=3$: $f(3)=4(3)-15=12-15=-3$. We draw an open circle at $(3, -3)$ (since $x>3$ is the domain). Then find another point: for $x=5$, $f(5)=4(5)-15=20-15=5$. Draw a line from the open circle at $(3, -3)$ through $(5, 5)$ extending to the right.

Answer:

1. A horizontal line at $y=-4$ from $x=-10$ to an open endpoint at $(-5, -4)$.
2. A line starting at an open endpoint at $(3, -3)$ passing through $(5, 5)$ and extending rightward.