Q 21. - Precalculus Enhanced with Graphing Utilities

Question

The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. 

Step-by-Step Solution

Answer

No, the given function is not one-to-one.

Step 1. Definition

A function is said to be one-to-one if any two different inputs in the domain correspond to two different outputs in the range.  

The horizontal line test checks if a function is one-to-one. A one-to-one function has only one x-value for each y-value. If a horizontal line passes through a graph more than once, the function can't be one-to-one. 

Step 2. Explanation

Use horizontal line test 

The given function is not one-to-one because horizontal line $y=1$ intersects the graph twice at $\left(-1,1\right)$ and $\left(1,1\right)$.