Question

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

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

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.
(graph axes with x from -10 to 10 and y from -10 to 10)

Explanation:

Step1: Analyze left piece

For \(x \leq -1\), \(f(x)=2x+5\). At \(x=-1\): \(y=2(-1)+5=3\) (closed dot). Slope=2, so line extends left.

Step2: Analyze right piece

For \(x > 5\), \(f(x)=-2\). At \(x=5\): open dot (since \(x>5\)) at \((5,-2)\). Horizontal line extends right.

Step3: Note gap

No definition between \(x=-1\) and \(x=5\), so no graph there.

Answer:

(Graph description: Left segment: line \(y=2x+5\) from \(x=-\infty\) to \(x=-1\) (closed dot at \((-1, 3)\)); Right segment: horizontal line \(y=-2\) from \(x=5\) to \(x=\infty\) (open dot at \((5, -2)\)); No graph between \(x=-1\) and \(x=5\))