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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 used to check if a graph represents a function. If we can draw a vertical line that intersects the graph more than once, the graph does not represent a function since that would mean one input ('x' value) is linked to more than one output ('y' value).

Step by step solution

01

Understanding Vertical Line Test

The Vertical Line Test is a visual way to use a vertical line to determine if a graph represents a function. A function is a particular type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).
02

Defining the Rule of Vertical Line Test

The rule of Vertical Line Test is simply stated as: If any vertical line intersects the graph more than once, then the graph does not represent a function. This is because, if the vertical line intersects the graph at more than one point, it means that a single input ('x' value) has more than one output ('y' value).
03

Applying the Vertical Line Test

If you are given a graph and want to use the Vertical Line Test to check if the graph represents a function, you need to draw or visualize vertical lines across the graph. If there's any vertical line that intersects the graph at more than one point, the graph does not represent a function. Otherwise, it does.

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