Question

give a rule of the piecewise - defined function. give the domain and the range.
what is the rule? select the correct choice below and fill in the answer boxes within your choice.
a. $f(x)=\

$$\begin{cases}\\square & \\text{if } x < \\square \\\\ \\square & \\text{if } x \\geq \\square \\end{cases}$$

$
b. $f(x)=\

$$\begin{cases}\\square & \\text{if } x \\leq \\square \\\\ \\square & \\text{if } x > \\square \\end{cases}$$

$

Explanation:

Step1: Identify first piece of function

Looking at the graph, for $x \leq 1$, the horizontal line is at $y=1$.

Step2: Identify second piece of function

For $x > 1$, the horizontal line is at $y=-1$.

Step3: Match to correct option

This matches option B's structure.

Step4: Find domain

All real numbers are covered on the x-axis, so domain is $(-\infty, \infty)$.

Step5: Find range

The only y-values are 1 and -1, so range is $\{-1, 1\}$.

Answer:

Rule:

B. $f(x)=

$$\begin{cases} 1 & \text{if } x \leq 1 \\ -1 & \text{if } x > 1 \end{cases}$$

$

Domain:

$(-\infty, \infty)$

Range:

$\{-1, 1\}$