Section 2.8 One-to-One Functions

Section 2.8
One-to-One Functions

One-to-One Function

In a one-to-one function, each x-value has only one y-value, and each y-value has only one x-value. That is, different values of the domain correspond to different values of the range.

Example 1

Determine if the relation given is one-to-one.

Multiple Choice

Determine if the relation given is one-to-one.

$$\left\{\left(6,3\right),\ \left(2,2\right),\ \left(-1,3\right),\ \left(0,9\right)\right\}$$

• Is a One-to-One Function

• Is not a One-to-One Function

Multiple Choice

Determine if the relation given is one-to-one.

$$\left\{\left(1,6\right),\ \left(2,2\right),\ \left(-1,3\right),\ \left(0,9\right)\right\}$$

• Is a One-to-One Function

• Is not a One-to-One Function

Horizontal Line Test

A function is one-to-one if every horizontal line intersects the graph of the function at most once. (Note:  It is a function, so it also must pass the vertical line test.)

Example 2

Determine if the relation given is one-to-one.

Multiple Choice

Determine if the relation given is one-to-one.

• Is a One-to-One Function

• Is not a One-to-One Function

Multiple Choice

Determine if the relation given is one-to-one.

• Is a One-to-One Function

• Is not a One-to-One Function