Question

f(x)=\

$$\begin{cases}-6&\\text{for }x\\leq - 1\\\\2x - 18&\\text{for }x>5\\end{cases}$$

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 $y = - 6$ for $x\leq - 1$

Draw a horizontal line $y=-6$. The left - hand endpoint is $(-1,-6)$ and it extends to the left (since $x\leq - 1$).

Step2: Graph $y = 2x - 18$ for $x>5$

First, find the value of $y$ when $x = 5$ for the line $y=2x - 18$. Substitute $x = 5$ into $y=2x - 18$, we get $y=2\times5-18=10 - 18=-8$. But our function is defined for $x>5$, so we start the line $y = 2x - 18$ just to the right of $x = 5$. The slope of the line $y=2x - 18$ is $m = 2$ and the $y$-intercept is $b=-18$. We can find another point by choosing $x = 6$, then $y=2\times6-18=12 - 18=-6$. So we draw a line with slope $2$ starting just to the right of $x = 5$ and extending to the right.

Answer:

The graph consists of a horizontal line $y = - 6$ for $x\leq - 1$ with a closed - circle at $(-1,-6)$ (because $x=-1$ is included in this part of the domain) and a line $y = 2x - 18$ for $x>5$ with an open - circle at $(5,-8)$ (because $x = 5$ is not included in this part of the domain) and a slope of $2$.