Question

graph the following function on the axes provided.
f(x)=\begin{cases}-2x&\text{for}& - 4leq x<3\\2&\text{for}&3 < xleq6end{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 $y = - 2x$ for $-4\leq x<3$

Find two points on $y=-2x$. When $x = - 4$, $y=-2\times(-4)=8$. When $x = 3$, $y=-2\times3=-6$. But for $y = - 2x$ in the given domain, the point $(3,-6)$ is an open - circle (since $x<3$) and the point $(-4,8)$ is a closed - circle (since $x\geq - 4$). Then draw a line segment connecting these two points (with the appropriate endpoints).

Step2: Graph $y = 2$ for $3

When $x = 3$, the point is an open - circle (since $x>3$) at $(3,2)$. When $x = 6$, the point is a closed - circle (since $x\leq6$) at $(6,2)$. Draw a horizontal line segment between these two points (with the appropriate endpoints).

Answer:

The graph consists of a line segment $y=-2x$ from the point $(-4,8)$ (closed - circle) to $(3, - 6)$ (open - circle) and a horizontal line segment $y = 2$ from the point $(3,2)$ (open - circle) to $(6,2)$ (closed - circle).