Question

what is the domain of the function shown in the graph below?

Explanation:

Step1: Identify excluded x-values

The graph has vertical dashed asymptotes at $x=-2$ and $x=7$, so these x-values are not in the domain.

Step2: Define valid x intervals

All real numbers less than -2, between -2 and 7, and greater than 7 are valid.

Answer:

All real numbers except $x=-2$ and $x=7$, or in interval notation: $(-\infty, -2) \cup (-2, 7) \cup (7, \infty)$