Question

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

Explanation:

Step1: Recall vertical - line test

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

Step2: Analyze first graph

For the first graph (a straight - line with a negative slope), any vertical line will intersect it at most once. So, it is a function.

Step3: Analyze second graph

In the second graph, there is a vertical asymptote. But still, any vertical line will intersect the graph at most once. So, it is a function.

Step4: Analyze third graph

For the third graph, a vertical line can be drawn that will intersect the graph at two points. So, it is not a function.

Step5: Analyze fourth graph

In the fourth graph (a V - shaped graph), any vertical line will intersect it at most once. So, it is a function.

Answer:

The first, second, and fourth relations are functions.