15. which of the following graphs represents a functional relationship between x and y?

15. which of the following graphs represents a functional relationship between x and y?

15. which of the following graphs represents a functional relationship between x and y?

Answer

Explanation:

Step1: Recall the vertical line test

A relation is a function if for every (x -) value there is exactly one (y -) value. The vertical line test states that if a vertical line intersects the graph of a relation at more than one point, the relation is not a function.

Step2: Analyze each graph

  • Graph A: If we draw a vertical line, it will intersect the graph at only one point for any (x) in the domain of the relation.
  • Graph B: A vertical line (for some (x) values) will intersect the graph at two points.
  • Graph C: A vertical line (for some (x) values) will intersect the graph at two points.
  • Graph D: A vertical line (for some (x) values) will intersect the graph at two points.

Answer:

A.