Question

does the graph given to the right represent a function? explain. choose the correct answer below. a. the graph represents a function because for every x - value of input, there is exactly one y - value of output. b. the graph does not represent a function because there is at least one x - value of input that has more than one y - value of output. c. the graph does not represent a function because for every x - value of input, there is more than one y - value of output. d. the graph represents a function because there is at least one x - value of input that has exactly one y - value of output.

Explanation:

Step1: Recall function definition

A relation is a function if for each input $x$-value, there is exactly one output $y$-value.

Step2: Apply vertical - line test concept

The vertical - line test states that if any vertical line drawn on the graph of a relation intersects the graph at more than one point, the relation is not a function. In other words, for every $x$ - value in the domain, there must be exactly one $y$ - value in the range.

Answer:

A. The graph represents a function because for every x - value of input, there is exactly one y - value of output.