Question

the domain of the piecewise function is $(-infty,infty)$
a. graph the function
b. use your graph to determine the functions range.
$f(x)=\

$$\begin{cases}\\ \\ \\ 3\\ \\ \\text{if}\\ x\\leq -2\\\\ -3\\ \\ \\text{if}\\ x > -2\\end{cases}$$

$

a. choose the correct graph below.
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

Explanation:

Step1: Analyze first piece of function

For $x \leq -2$, $f(x)=3$. This is a horizontal line at $y=3$, with a closed dot at $x=-2$ (since $x=-2$ is included).

Step2: Analyze second piece of function

For $x > -2$, $f(x)=-3$. This is a horizontal line at $y=-3$, with an open dot at $x=-2$ (since $x=-2$ is not included).

Step3: Match to given graphs

Find the graph with closed dot at $(-2, 3)$ and open dot at $(-2, -3)$, with horizontal lines $y=3$ (left of $x=-2$) and $y=-3$ (right of $x=-2$).

Step4: Determine the range

The function only takes two values: 3 and -3.

Answer:

a. A. <The graph with closed dot at (-2, 3) and open dot at (-2, -3), horizontal line y=3 for x ≤ -2 and y=-3 for x > -2>
b. $\{-3, 3\}$