Problem 72 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

The horizontal line test is a method used to determine if a function has an inverse that is also a function. It's conducted by drawing a horizontal line parallel to the x-axis across a function's graph. If this line intersects the graph more than once, it implies the function does not have an inverse that is also a function. If it intersects at most once for each height, the function does have an inverse that is also a function.

Step 1: Definition of Horizontal Line Test

The horizontal line test is a method used to determine whether a function has an inverse that is also a function. It involves drawing a horizontal line across the graph of the function. If the line intersects the graph in more than one place, then the original function does not have an inverse that is a function.

Step by step procedure

In mathematical terms, to conduct the horizontal line test, one will draw a line which is horizontally parallel to the x-axis. You analyze this line against the graph of the given function. This line should be able to glide or move along the y-axis (upwards and downwards).

Step 3: Interpreting the Horizontal Line Test

As you conduct the horizontal line test, if this horizontal line intersects the graph of the given function at more than one point, then you conclude that the function fails the horizontal line test, indicating that the function doesn't have an inverse that is a function. However, if the horizontal line crosses the graph at most one time for each height - the graph passes the horizontal line test. This indicates that the function has an inverse that is also a function.