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. no, the graph is not a function because a vertical line x = 2 intersects the graph at only one point. c. no, the graph is not a function because a vertical line x = 2 intersects the graph at two points. d. yes, the graph is a function because every vertical line intersects the graph in more than one point.

Explanation:

Step1: Apply vertical - line test

A graph represents a function if any vertical line intersects the graph at most once. For the given graph, any vertical line will intersect the graph in at most one point.

Step2: Analyze options

Option A correctly states that the graph is a function because every vertical line intersects the graph in at most one point. Option B's reasoning is incorrect as a vertical line intersecting at one point is a sign of a function, not non - function. Option C is wrong since no vertical line intersects the graph at two points. Option D is wrong because a function has vertical lines intersecting at most one point, not more than one point.

Answer:

A. Yes, the graph is a function because every vertical line intersects the graph in at most one point.