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Chapter 2: Problem 72

What is the horizontal line test and what does it indicate?

Short Answer

Expert verified
The horizontal line test is a method to check if a function has an inverse that is also a function. If any horizontal line intersects the function's graph more than once, the function fails the horizontal line test, indicating that it does not have an inverse that is also a function. However, if no horizontal line intersects the graph more than once, then the function passes the test and it does have an inverse that is also a function.

Step by step solution

01

Understanding the Horizontal Line Test

The horizontal line test is a test used to determine if a function has an inverse that is also a function. This test involves visualizing or sketching the graph of the function and imagining a horizontal line passing through it.
02

Applying the Horizontal Line Test

To apply the test, you make an imaginary sweep of the function's graph with a horizontal line. Consider every possible horizontal line that can be drawn across the graph.
03

Interpreting the Results

If any horizontal line intersects the function's graph more than once, then the function fails the horizontal line test and does not have an inverse that is also a function. If no horizontal line intersects the graph more than once, the function passes the horizontal line test and does have an inverse that is also a function.

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Most popular questions from this chapter

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{array}{r} {x^{2}+y^{2}=9} \\ {x-y=3} \end{array}$$

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