Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?

Question

On a coordinate plane, a circle is centered around (0, 0).
The graph is not a function of x because the line x = 0 intersects the graph at two points.
The graph is a function of x because the line x = 5 does not intersect the graph.
The graph is not a function of x because the line y = 0 intersects the graph at two points.
The graph is a function of x because the line y = 5 does not intersect the graph.

Answer 1

The best statement that illustrates using the vertical line test to determine if the graph is a function of x is:

"The graph is not a function of x because the line x = 0 intersects the graph at two points."

This statement accurately reflects the vertical line test, which states that if any vertical line intersects the graph at more than one point, then the graph does not represent a function of x. Since the graph described is a circle centered at (0, 0), the vertical line x = 0 (the y-axis) would intersect the circle at two points, indicating that for that x-value, there are two corresponding y-values. Therefore, the graph is not a function of x.