Question

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which of these relations is a function?

Explanation:

Step1: Recall function definition

A relation is a function if every input (x-value) has exactly one output (y-value). The vertical line test checks this: any vertical line drawn on the graph intersects the curve at most once.

Step2: Test each graph

• Top-left parabola: Any vertical line intersects it once. Passes test.
• Top-right curve: A vertical line intersects it twice. Fails test.
• Bottom-left circle: A vertical line intersects it twice. Fails test.
• Bottom-right ellipse: A vertical line intersects it twice. Fails test.

Answer:

The top-left downward-opening parabola (the first graph in the top row) is a function.