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Chapter 1: 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 used to determine if a graph represents a function by checking that for every 'x' value, there is only one 'y' value. If any vertical line drawn through the graph intersects the graph at more than one point, then the graph does not represent a function as it shows that an 'x' value is associated with multiple 'y' values.

Step by step solution

01

Understand the concept of a function

In mathematics, a function can be thought of as a rule that assigns one output to each input. In the context of a graph, each 'x' value (horizontal coordinate) corresponds to exactly one 'y' value (vertical coordinate). If any 'x' value is assigned more than one 'y' value, then the rule does not represent a function.
02

Understanding the vertical line test

The vertical line test is a simple, visual way to determine if a graph represents a function. It involves imagining or drawing a vertical line moving across the x-axis of the graph. If the line ever crosses over the graph more than once, then the graph does not depict a function.
03

Using the vertical line test to determine if a graph represents a function

To use the vertical line test, simply imagine or draw a vertical line on the graph and slowly move it from one end of the x-axis to the other. If the line only ever intersects the graph at one point as it moves, then the graph represents a function. However, if at any stage the line crosses the graph at more than one point, then the graph does not represent a function.

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