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
is the graph that of a function?
a. yes, the graph is a function because every vertical line intersects the graph in more than one point.
b. no, the graph is not a function because a vertical line x = 6 intersects the graph at two points.
c. yes, the graph is a function because every vertical line intersects the graph in at most one point.
d. no, the graph is not a function because a vertical line x = 6 intersects the graph at only one point.

Explanation:

Step1: Recall 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.

Step2: Analyze the given graph

If a vertical line can be drawn such that it intersects the graph at more than one point, then the graph is not a function. In the case of the given graph, we can find a vertical line (for example, \(x = 6\)) that intersects the graph at two points. So, the graph is not a function.

Answer:

B. No, the graph is not a function because a vertical line \(x = 6\) intersects the graph at two points.