A coordinate plane shows both the axes ranging from negative 12 to 12 in increments of 1. A closed point and an arrow are drawn on the graph. A rightward, decreasing, arrow is drawn from a closed point at left parenthesis negative 7 comma 5 right parenthesis. The arrowhead ends at left parenthesis 6 comma negative 6 right parenthesis.

Question

Describe the domain of the linear function on the graph. Enter the option number of the correct solution.

Option #1: x≥−7


Option #2: x≥6


Option #3: x≤−7


Option ?

Answer 1

To determine the domain of the linear function represented by the arrow from the point \((-7, 5)\) to \((6, -6)\), we need to analyze the endpoints of the arrow.

The arrow starts at \((-7, 5)\) and points rightward toward \((6, -6)\). Since the arrow is decreasing and extends to the right, the x-values of the function will range from the left endpoint \(-7\) to the right endpoint \(6\).

Thus, the domain of this linear function is all x-values greater than or equal to \(-7\) and less than or equal to \(6\).

However, since the options provided seem to focus exclusively on parts of the domain, and since the most relevant portion concerning starting point is the left endpoint, the correct option that describes part of this domain is:

Option #1: \(x \ge -7\)

This option indicates that the function begins at \(-7\) and includes values greater than \(-7\). Of course, the x-values also cap at \(6\), but that is not included in the options.