Question

find the domain and the range of the relation. use the vertical line test to determine whether the graph is the graph of a function.
choose the correct domain below.
oa. $(-\infty, -5 \cup 5, \infty)$
ob. $-5, 5$
oc. $(-\infty, \infty)$
od. none of the above

Explanation:

Step1: Recall Domain Definition

The domain of a graph is the set of all x - values the graph covers. For a function (or relation) represented graphically, we look at the horizontal extent.

Step2: Analyze the Graph's Horizontal Extent

From the options, option C is \((-\infty,\infty)\), which would mean the graph extends infinitely in both horizontal directions. If the graph (even with the visible part and considering the nature of the curve, maybe a periodic or a curve that doesn't have horizontal restrictions) covers all real numbers for x, then the domain is all real numbers. Option A is a union of two intervals excluding (-5,5), option B is the closed interval [-5,5]. If the graph is such that there are no restrictions on the x - values (e.g., a sine - like curve that goes on forever horizontally, or a polynomial of even or odd degree with no horizontal asymptotes limiting the domain), then the domain is \((-\infty,\infty)\).

Answer:

C. \((-\infty,\infty)\)