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 the graph at most once.

Step2: Analyze the first graph

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

Step3: Analyze the second graph

For the second graph (top - right, the line), applying the vertical line test, any vertical line will intersect the line at most once. So it is a function.

Step4: Analyze the third graph

For the third graph (bottom - left, the curve), applying the vertical line test, any vertical line will intersect the curve at most once. So it is a function.

Step5: Analyze the fourth graph

For the fourth graph (bottom - right, the ellipse), there exist vertical lines that intersect the ellipse at two points. So it is not a function.

Answer:

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