To determine the domain of the linear function shown in the graph, we note that the line extends through the points \((-9, -5.3)\) and \((7.5, 4.5)\).
The x-coordinates of the endpoints of the line segment are \(-9\) and \(7.5\). Since the line is drawn as a solid line, it includes both endpoints, meaning that the x-values can take any value from \(-9\) to \(7.5\), including \(-9\) and \(7.5\).
Thus, the domain of the function can be described as:
\(-9 \leq x \leq 7.5\)
Since this isn't among the offered choices, we should choose the response that accurately captures the relevant x-values without exceeding the interval given:
The most appropriate choice from the given responses is:
−9≤x≤7 negative 9 less-than-or-equal-to x less-than-or-equal-to 7
However, note that one endpoint is incorrect as the maximum x-value is actually \(7.5\). But \(7\) is included in the options, suggesting a possible error in the choices provided.
If specifically asked to account for \(7.5\), a fit wasn’t offered. The closest answer regarding established boundaries, assuming proper x-range detail wasn't indicated for options is:
−9≤x≤7 would be chosen, acknowledging the mentioned flaw with \(7.5\) in relation to potential correctness adjustments if possible re-evaluation filtered from the full set of graphical indications.