# How to prove a function is one to one

College algebra students learn How to prove a function is one to one, and manipulate different types of functions.

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## How can we prove a one-to-one and onto function?

So, for two different values of x there can be same value of y, making it a many-to-one function. e.g., let f (x) = x^2 dy/dx = 2x so, for negative x, the slope is negative and for positive x the slope

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## 1 One-To-One Functions

So now we can use this definition to develop a simple test. If f (a) = f (b), this implies that a = b, if the function is one-to-one. So what we can do is plug in an a for x and plug in a b