Answer:
d. x > 2 or x < -2
Explanation:
Domain describes the range of x-values in a function.
Domain
The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.
By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.
Included Values
We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.