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Chapter 2: Problem 114

Explain how the vertical line test is used to determine whether a graph represents a function.

Short Answer

Expert verified
The vertical line test is a way to determine whether a graph represents a function or not. It entails drawing a vertical line across the graph and if at any point, the line crosses the graph at more than one point, it means that for one value of input (x-coordinate), we are getting more than one output (y-coordinate) thus, it doesn't represent a function.

Step by step solution

01

Understand the concept of a function

A function is an association that assigns exactly one output to each input. In simpler words, for every value of x, there is only one corresponding value of y.
02

Explain the vertical line test

The vertical line test is a method to determine if a graph represents a function. This is done by visually checking if a vertical line intersects the graph at more than one point. If it does at any point, then the graph does not represent a function.
03

Applying the vertical line test

Let's say you have a graph drawn on a Cartesian plane. To apply the vertical line test, try to imagine or draw a vertical line that moves across the graph. If at any position, the vertical line touches the graph at more than one point, then the graph does not represent a function since it breaks the rule of having one output for each input.

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