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.

Explanation:

Step1: Recall vertical - line test

The vertical - line test states that a graph is a function if and only if every vertical line intersects the graph in at most one point.

Step2: Analyze the given options

Option A is correct as it correctly states the condition for a graph to be a function according to the vertical - line test. Option B is incorrect because if a vertical line intersects the graph in more than one point, it is not a function. Option C is correct in its reasoning for the graph not being a function. Option D is incorrect because if a vertical line intersects the graph at only one point, it is consistent with the graph being a function, not the opposite.

Answer:

C. No, the graph is not a function because a vertical line x = 6 intersects the graph at two points.