Use the image to answer the question.

Question

A coordinate plane shows both the axes ranging from negative 12 to 12 in increments of 1. An upward solid line with arrows at both ends passes through origin and extends to quadrants 1 and 3. The arrow points to the unmarked points left parenthesis negative 9 comma negative 5.3 right parenthesis and left parenthesis 7.5 comma 4.5 right parenthesis.

Describe the domain of the linear function on the graph.

(1 point)
Responses

x
is all real numbers.
x is all real numbers.

−9≤x≤7
negative 9 less-than-or-equal-to x less-than-or-equal-to 7

−9<x<7
negative 9 less than x less than 7

x≥−9
x greater-than-or-equal-to negative 9

Answer 1

To determine the domain of the linear function described in the graph, we note that it is a solid line that extends from the point \((-9, -5.3)\) on the left to the point \((7.5, 4.5)\) on the right. Since the line is solid, it includes both endpoints.

Thus, the domain of the function is all \(x\) values from \(-9\) to \(7.5\) inclusive, which can be described by the inequality:

\[-9 \leq x \leq 7.5\]

However, since the provided options do not include \(7.5\) specifically, and since the closest option that accurately reflects the left endpoint is:

\[-9 \leq x < 7\]

This cannot be correct either. The best fitting response from the options provided would be:

\[-9 \leq x \leq 7\]

Thus, if careful, the answer should reflect that the function exists in this interval, but if limited to available responses according to provided disparities, the most concise representation while remaining inclusive is:

x ≥ -9 (implying from that point onward, but should acknowledge a range extending toward \(+\infty\) accurate to initial details from graph confines).

Nonetheless, without leaning on selectivity, describing the real maximal content details remains paramount adhering toward actual usage in analytical value concerns in function directionally engaged.