Question - Determining the Domain and Range from a Graph

The graph shows a function with two distinct parts. The first part is decreasing and the second part is increasing. There is a break in the graph where the function is not defined.

To find the domain, we look for the x-values that the function covers. By observing the graph, we see that the function is defined for all x except for a portion where x is between -4 and 3. Thus the domain is \( x < -4 \) or \( x > 3 \).

The range of a function is the set of all possible output values (y-values), which result from using the function's formula. By examining the graph, we see that as \( x \) approaches -4 from the left, the y-values decrease without bound, and as \( x \) approaches 3 from the right, the y-values increase without bound. Therefore, the range of the function is all real numbers, which can be denoted as \( -\infty < y < \infty \) or simply \( y \in \mathbb{R} \).