Question

which of these relations is a function?

Explanation:

Step1: Recall function vertical line test

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

Step2: Test top-left ellipse

Vertical lines will intersect the ellipse at 2 points, so it is not a function.

Step3: Test top-right curve

All vertical lines intersect the curve at most once, so it passes the test.

Step4: Test bottom-left graph

Vertical lines (e.g., $x=-2$) intersect the graph at 2 points, so it is not a function.

Step5: Verify bottom-right line

All vertical lines intersect the line at exactly 1 point, so it passes the test.

Answer:

The top-right curve and the bottom-right line are functions.