Question

which of these relations is a function?

Explanation:

Step1: Recall vertical line test

A relation is a function if any vertical line drawn on its graph intersects the graph at most once.

Step2: Test top-left graph

Any vertical line cuts this curve at only one point. It passes the test.

Step3: Test top-right graph

A vertical line (e.g., $x=0$) cuts the circle at two points. It fails the test.

Step4: Test bottom-left graph

Any vertical line cuts this parabola at only one point. It passes the test.

Step5: Test bottom-right graph

A vertical line cuts this curve at two points. It fails the test.

Answer:

The top-left graph (the upward-opening curved relation) and the bottom-left graph (the downward-opening parabola) are functions.