One of the functionsis one to one , and the other is not.

Which function below is 1 to 1?

Function #2 on the right side is the one to one function . In a one to one function, every element in the range corresponds with one and only one element in the domain.

So, #1 is not one to one because the range element.
5 goes with 2 different values in the domain (4 and 11).

Diagram 1

How to know if $$ f(x) $$ is 1 to 1?

To be a function

Only one thing must be true : each element in domain must go to a unique range element. ( prior lesson)

Second: This is the new part. each element in range must go to a unique element in the domain.

Diagram 3

So, there is one new characteristic that must be true for a function to be one to one. This new requirement can also be seen graphically when we plot functions, something we will look at below with the horizontal line test.