Problem 72 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

A horizontal line test is used to determine if a function is injective. If at any point the horizontal line touches the graph more than once when moving the line vertically up and down the graph, the function is non-injective.

Step 1: What is the Horizontal Line Test?

The horizontal line test is a graphical method used to determine whether a function is injective (also known as one-to-one), i.e., every y-value has a unique x-value associated with it in the function.

Step 2: How to Perform the Horizontal Line Test?

To perform the horizontal line test, a horizontal line is drawn through the graph of the function. The line is moved up and down the graph to see if the line at any point touches the graph more than once.

Step 3: What does the Findings of Horizontal Line Test indicate?

If the horizontal line only touches the graph at one point at all levels of the graph, the function passes the test; it is injective. However, if the line touches the graph at more than one point at any level, the function is non-injective. This would mean that there are at least two x-values for one y-value in the function.