Question

which of these relations is a function?

Explanation:

A relation is a function if every input (x-value) has exactly one output (y-value), which can be tested with the Vertical Line Test: any vertical line drawn on the graph intersects the curve at most once.

1. Top-left graph: All vertical lines intersect the parabola at most once, so it passes the test.
2. Top-right graph: A vertical line will intersect the S-shaped curve twice, so it fails.
3. Bottom-right graph: A vertical line will intersect the oval twice, so it fails.

Answer:

The top-left parabola graph (the U-shaped curve crossing the y-axis and opening upwards) is a function.