Question

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

Explanation:

Step1: Apply Vertical Line Test

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

Step2: Check Top-Left Graph

Any vertical line intersects this straight line only once. So it is a function.

Step3: Check Top-Right Graph

Any vertical line intersects this curve only once. So it is a function.

Step4: Check Bottom-Left Graph

Any vertical line intersects this parabola only once. So it is a function.

Step5: Check Bottom-Right Graph

A vertical line can be drawn that intersects this circle twice. So it is NOT a function.

Answer:

The top-left linear graph, top-right curved graph, and bottom-left parabolic graph are functions.