Question

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

Explanation:

Step1: Recall Vertical Line Test

A relation is a function if no vertical line intersects its graph more than once.

Step2: Analyze Top - Left Graph

Draw a vertical line (mentally) through the graph. Each vertical line intersects the graph at most once. So it is a function.

Step3: Analyze Top - Right Graph

Draw a vertical line. There are vertical lines that intersect this graph more than once (e.g., the y - axis intersects it at two points). So it is not a function.

Step4: Analyze Bottom - Left Graph

Draw a vertical line. Each vertical line intersects the graph at most once. So it is a function.

Step5: Analyze Bottom - Right Graph

Draw a vertical line. Each vertical line intersects the graph at most once. So it is a function.

Answer:

The Top - Left Graph, The Bottom - Left Graph, The Bottom - Right Graph