Question

Find the domain of the function shown on the graph

Answer 1

Answer: C) $-\infty < x < \infty$

This is the set of all real numbers

How do we know this? Because of how the arrows indicate the graph goes on forever in both left and right directions. We can plug in any x value we want without any restrictions. There isn't anything like division by zero errors to worry about here. There are no vertical asymptotes, but there is a horizontal asymptote at y = 3.

In interval notation, the domain is written as $(-\infty, \infty)$

In set-builder notation, you could write $\{x|x\in\mathbb{R}\}$ for the domain. The R stands for "real numbers".