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 at most one point.
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 = 6 intersects the graph at two points.
d. no, the graph is not a function because a vertical line x = 6 intersects the graph at only one point.
(a) the domain is (type your answer in interval notation.)

Explanation:

Step1: Recall vertical - line test

A graph represents a function if and only if every vertical line intersects the graph at most once. Since a vertical line \(x = 6\) intersects the graph at two points, the graph is not a function.

Step2: Find the domain

The domain is the set of all \(x\) - values for which the graph exists. Looking at the graph, the \(x\) - values range from \(-\infty\) to \(\infty\). In interval notation, the domain is \((-\infty,\infty)\).

Answer:

No, the graph is not a function because a vertical line \(x = 6\) intersects the graph at more than one point.
(a) \((-\infty,\infty)\)