Question

determine whether the following graph represents a function.
the graph represent a function because is mapped to .

Explanation:

Step1: Recall the vertical line test

A graph represents a function if every vertical line intersects the graph at most once. This means each \( x \)-value has at most one \( y \)-value.

Step2: Apply the vertical line test to the given graph

Looking at the graph, for any vertical line (any specific \( x \)-value), we can see that it will intersect the graph at only one point. For example, take \( x = 0 \), it intersects at \( y = 2 \); take \( x = 1 \), it intersects at some unique \( y \)-value, and so on. There is no \( x \)-value that has more than one \( y \)-value associated with it. So the graph passes the vertical line test.

Answer:

The graph \(\boldsymbol{\text{does}}\) represent a function because \(\boldsymbol{\text{each } x\text{-value}}\) is mapped to \(\boldsymbol{\text{exactly one } y\text{-value}}\).