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 (top - left)

Draw a vertical line anywhere on the graph. It will intersect the parabola at most once. So this is a function.

Step3: Analyze the second graph (top - right)

Using the vertical line test, any vertical line will intersect this graph at most once. So this is a function.

Step4: Analyze the third graph (bottom - left)

A vertical line (e.g., along the y - axis) will intersect this graph twice. So this is not a function.

Step5: Analyze the fourth graph (bottom - right)

Using the vertical line test, any vertical line will intersect this line (a linear graph) at most once. So this is a function.

Answer:

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