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 (top - left)

Draw a vertical line anywhere on the graph. It will intersect the graph at only one point. So, it passes the vertical line test.

Step3: Analyze the second graph (top - right)

Draw a vertical line anywhere on the graph. It will intersect the graph at only one point. So, it passes the vertical line test.

Step4: Analyze the third graph (bottom - left)

Draw a vertical line anywhere on the graph. It will intersect the graph at only one point. So, it passes the vertical line test.

Step5: Analyze the fourth graph (bottom - right)

Draw a vertical line. It will intersect the graph at more than one point. So, it fails the vertical line test.

Answer:

The top - left graph, the top - right graph, and the bottom - left graph.