Question

which of these relations is a function?

Explanation:

Step1: Recall function definition

A relation is a function if for every x - value there is exactly one y - value. We can use the vertical line test. If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Step2: Analyze first graph

The first graph is an ellipse. A vertical line can intersect the ellipse at two points. So, it is not a function.

Step3: Analyze second graph

The second graph has a "V - shape" with a sharp turn. A vertical line can intersect it at two points in some places. So, it is not a function.

Step4: Analyze third graph

The third graph is a straight - line. For any vertical line drawn, it will intersect the line at exactly one point. So, it is a function.

Step5: Analyze fourth graph

The fourth graph is an "S - shape" curve. A vertical line can intersect it at two points in some places. So, it is not a function.

Answer:

The third relation (the straight - line graph) is a function.