Question

question 19, 3.2.19
part 1 of 5
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.

Explanation:

Step1: Recall vertical - line test

A graph represents a function if and only if every vertical line intersects the graph at most once.

Step2: Analyze given vertical - line

Given that the vertical line $x = - 3$ intersects the graph at two points. So, 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.