Question

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

Explanation:

Step1: Identify excluded x-value

The graph has a vertical dashed line at $x=-4$, meaning $x=-4$ is not in the domain.

Step2: Identify valid x-values

The graph exists for all x-values greater than $-4$, and all x-values less than $-4$.

Step3: Write domain in interval form

Combine the valid intervals: $(-\infty, -4) \cup (-4, \infty)$

Answer:

All real numbers except $x=-4$, or in interval notation: $(-\infty, -4) \cup (-4, \infty)$