Question

determine whether the graph is that of a function by using the vertical - line test. in either case, use the graph to find the following.
(a) the domain and range
(b) the intercepts, if any.
(c) any symmetry with respect to the x - axis, y - axis, or the origin
does the graph represent a function?
a. no, the graph is not a function because a vertical line x = - 3 intersects the graph at two points
b. yes, the graph is a function because every vertical line intersects the graph in more than one point.
c. no, the graph is not a function because a vertical line x = - 3 intersects the graph at only one point.
d. yes, the graph is a function because every vertical line intersects the graph in at most one point.
(a) the domain is
(type your answer in interval notation.)

Explanation:

Step1: Apply vertical - line test

The vertical - line test states that a graph represents a function if and only if every vertical line intersects the graph at most once. If a vertical line intersects the graph at more than one point, then for a single \(x\) - value, there are multiple \(y\) - values, which violates the definition of a function. Here, since a vertical line \(x=-3\) intersects the graph at two points, the graph is not a function.

Answer:

A. No, the graph is not a function because a vertical line \(x = - 3\) intersects the graph at two points