How to determine if a function is one-to-one?

First determine if it's a function to begin with, once we know that we are working with function to determine if it's one to one. Then only one value in the domain can correspond to one value in the range.

Example of one to one function

You can also quickly tell if a function is one to one by analyzing it's graph with a simple horizontal-line test. If the horizontal line only touches one point, in the function then it is a one to one function other wise it's not.

Example of a the horizontal line test

The proof for this is a quite easy to see on a graph and algebraically.

Determine if one to one algebraically

As you can see 16 lives in two places in the range meaning it's not a one to one function.