Question

use the vertical line test to determine whether the graph shown to the right is the graph of a function.

choose the correct answer below

a. the given graph is a graph of a function because a vertical line can be drawn that will intersect this graph more than once.

b. the given graph is a graph of a function because no vertical line will intersect this graph more than once.

c. the given graph is not a graph of a function because a vertical line can be drawn that will intersect this graph more than once.

Explanation:

The vertical line test states that a graph represents a function if and only if no vertical line intersects the graph more than once. For the given circle graph, we can draw a vertical line (e.g., a line slightly left of the x-axis intercept on the right) that crosses the circle at two distinct points. This violates the vertical line test, so the graph is not a function.

Answer:

C. The given graph is not a graph of a function because a vertical line can be drawn that will intersect this graph more than once.