Which statement best describes the graph of a function?

Which statement best describes the graph of a function?

• A. The graph passes the horizontal line test.
• B. The graph may have multiple y-values for a single x-value.
• C. The graph passes the vertical line test.
• D. The graph can intersect a vertical line more than once.

Answer: (C)

For a graph to represent a function, every input value must have exactly one output value. Geometrically, this means a vertical line drawn anywhere on the graph should intersect the graph at most once. If a vertical line hits the graph more than once, that would mean a single x-value is associated with multiple y-values, which isn’t allowed for a function. So the graph that passes the vertical line test correctly embodies the idea that each input has a single output. The horizontal line test is about being one-to-one, which is a stronger condition than simply being a function, and a graph can pass the vertical line test without meeting that stricter criterion.

For a graph to represent a function, every input value must have exactly one output value. Geometrically, this means a vertical line drawn anywhere on the graph should intersect the graph at most once. If a vertical line hits the graph more than once, that would mean a single x-value is associated with multiple y-values, which isn’t allowed for a function. So the graph that passes the vertical line test correctly embodies the idea that each input has a single output. The horizontal line test is about being one-to-one, which is a stronger condition than simply being a function, and a graph can pass the vertical line test without meeting that stricter criterion.