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 x less than 7

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

x≥−9
x greater-than-or-equal-to negative 9
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Answer 1

The linear function shown in the graph extends from the point \((-9, -5.3)\) in quadrant 3 to the point \((7.5, 4.5)\) in quadrant 1. Since the line passes through the origin and the points \((-9, -5.3)\) and \((7.5, 4.5)\), the domain of the linear function includes all \(x\) values between \(-9\) and \(7.5\), inclusive of both endpoints.

Thus, the correct description of the domain of the linear function on the graph is:

−9 ≤ x ≤ 7.5

Given that this option is not explicitly listed among your choices, it appears that the most relevant choice that aligns with the endpoints mentioned, while including \(-9\), is:

−9 ≤ x ≤ 7.

This indicates that \(x\) can take any real value from \(-9\) to \(7\) inclusive, with \(7\) being effectively the ending point of the specified range.

If you just meant for the endpoints presented, and considering your options, the best selection might be:

−9 ≤ x ≤ 7.

Please confirm the exact choices presented in order to finalize the option as per your task requirements.