Question

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

Explanation:

Step1: Identify valid x-values left segment

The left curve has an open endpoint at $x=-8$, and extends left (to negative infinity). So this interval is $(-\infty, -8)$.

Step2: Identify valid x-values right segment

The right curve has an open endpoint at $x=-4$, and extends right (to positive infinity). So this interval is $(-4, \infty)$.

Step3: Combine the intervals

The domain is the union of the two valid x-intervals.

Answer:

$(-\infty, -8) \cup (-4, \infty)$