If a relation's graph fails the Vertical Line Test, what is true?

If a relation's graph fails the Vertical Line Test, what is true?

• A. It represents a function.
• B. It is linear.
• C. It is not a function.
• D. It must be a circle.

Answer: (C)

A relation is a function when every input has exactly one output. The Vertical Line Test is a quick way to check this: if a vertical line intersects the graph at more than one point, that input would have multiple outputs, which isn’t allowed for a function. So if the vertical line test fails, the graph cannot represent a function. The failure doesn’t pin down a specific shape—many nonfunctions exist, such as a circle or a vertical line—so the key point remains: not a function.

A relation is a function when every input has exactly one output. The Vertical Line Test is a quick way to check this: if a vertical line intersects the graph at more than one point, that input would have multiple outputs, which isn’t allowed for a function. So if the vertical line test fails, the graph cannot represent a function. The failure doesn’t pin down a specific shape—many nonfunctions exist, such as a circle or a vertical line—so the key point remains: not a function.