Question

graph the following function on the axes provided. $f(x)=\begin{cases}-3x - 6& \text{for }x < - 1\\-2x + 8& \text{for }x>5end{cases}$ 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: Find points for $y = - 3x - 6$ when $x < - 1$

Choose $x=-2$, then $y=-3\times(-2)-6=0$.

Step2: Analyze the end - point for $y = - 3x - 6$

Since $x < - 1$, when $x=-1$, $y=-3\times(-1)-6=-3$. The point $(-1, - 3)$ is an open - circle (not included in the graph of $y=-3x - 6$ for $x < - 1$).

Step3: Find points for $y=-2x + 8$ when $x>5$

Choose $x = 6$, then $y=-2\times6 + 8=-4$.

Step4: Analyze the end - point for $y=-2x + 8$

Since $x>5$, when $x = 5$, $y=-2\times5+8=-2$. The point $(5,-2)$ is an open - circle (not included in the graph of $y=-2x + 8$ for $x>5$).

Step5: Graph the lines

Draw a line for $y=-3x - 6$ with an open - circle at $(-1,-3)$ for $x < - 1$. Draw a line for $y=-2x + 8$ with an open - circle at $(5,-2)$ for $x>5$.

Answer:

The graph consists of a line $y=-3x - 6$ for $x < - 1$ (open - circle at $(-1,-3)$) and a line $y=-2x + 8$ for $x>5$ (open - circle at $(5,-2)$).