Question

Determine whether the function given by a graph is one-to-one.

Short answer

The resultant answer is not a one-to-one function.

Step-by-step solution

Given data

The given function \(f\) is one-to-one.

Concept of functions

The simplest definition is an equation will be a function if, for any \({\rm{x}}\) in the domain of the equation (the domain is all the \({\rm{x}}\)'s that can be plugged into the equation), the equation will yield exactly one value of \({\rm{y}}\) when we evaluate the equation at a specific \({\rm{X}}\).

Simplify the expression

Perform the horizontal line test for the given graph.

Draw a horizontal line in such a way that it passes through the curve as shown in Figure below.

From Figure, it is observed that the horizontal line intersects the curve exactly at two distinct points, which means it fails the horizontal line test.

Therefore, the function given by a graph is not a one-to-one function.