Question

which of these relations are functions? select all that apply.

Explanation:

Step1: Recall the vertical line test

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

Step2: Analyze the first graph

Draw (or imagine) vertical lines over the first graph. Each vertical line intersects the graph at only one point. So it passes the vertical line test.

Step3: Analyze the second graph

For the second graph, any vertical line will intersect it at most once. It passes the vertical line test.

Step4: Analyze the third graph

The third graph (parabola - like) also passes the vertical line test as vertical lines intersect it at one point.

Step5: Analyze the fourth graph

The fourth graph has a part where a vertical line would intersect it more than once (the triangular part). So it fails the vertical line test.

Answer:

The first graph, the second graph, the third graph