Question

1. the graph of piecewise function r is shown below.

select all that apply.

□ a. -4 < x < 0
□ b. -4 ≤ x < 0
□ c. -4 ≤ x ≤ 0
□ d. 1 < x < 5
□ e. 6 < x < 8
□ f. 4 ≤ x ≤ 5

Explanation:

Step1: Analyze left segment domain

The left horizontal segment has a closed dot at $x=-4$ and a closed dot at $x=0$, so its domain is $-4 \leq x \leq 0$.

Step2: Analyze middle segment domain

The middle rising segment has an open dot at $x=1$ and an open dot at $x=4$, so its domain is $1 < x < 4$ (not an option).

Step3: Analyze right segment domain

The right horizontal segment has a closed dot at $x=6$ and a closed dot at $x=8$, so its domain is $6 \leq x \leq 8$ (not an option).

Step4: Match to given options

Only the domain of the left segment matches option C, and no other segments match the remaining options.

Answer:

C. $-4 \leq x \leq 0$