Question

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

Explanation:

Step1: Recall the vertical line test

A relation is a function if no vertical line intersects its graph more than once.

Step2: Analyze the first graph

For the first graph (top - left), any vertical line will intersect it at most once. So it passes the vertical line test and is a function.

Step3: Analyze the second graph

For the second graph (top - right), there exists a vertical line that intersects it more than once. So it fails the vertical line test and is not a function.

Step4: Analyze the third graph (circle)

For the circle (bottom - left), a vertical line can intersect the circle at two points. So it fails the vertical line test and is not a function.

Step5: Analyze the fourth graph (circle)

For the bottom - right circle, a vertical line can intersect the circle at two points. So it fails the vertical line test and is not a function.

Answer:

The top - left graph (the graph with the V - shaped and linear part passing through the origin) is a function.