Question

1. which of the following represents the domain for the graph below?

a. ${-4 leq x leq 3}$
b. ${-4, -2, 0, 1, 3}$
c. ${0, 1, 2, 3, 4}$
d. ${x geq 0}$

Explanation:

Step1: Recall domain definition

The domain of a graph (of a discrete set of points, here) is the set of all \( x \)-values of the points.

Step2: Identify \( x \)-values from graph

Looking at the plotted points, their \( x \)-coordinates (from left to right) are: \( -4 \), \( -2 \), \( 0 \), \( 1 \), \( 3 \).

Step3: Match with options

• Option A: Interval for continuous domain, but the graph has discrete points, so A is wrong.
• Option B: Set \(\{-4, -2, 0, 1, 3\}\) matches the \( x \)-values of the points.
• Option C: \( x \)-values here don't include negative numbers like \(-4, -2\), so C is wrong.
• Option D: Interval for \( x \geq 0 \), but we have negative \( x \)-values (\(-4, -2\)), so D is wrong.

Answer:

B. \(\{-4, -2, 0, 1, 3\}\)