Algebra/Chapter 5/Functions

One-to-one function

A function that for every input there exists an output unique to that input.

Equivalently, we may say that a function $f$ is called one-to-one if for all $x,x^{\prime }\in A,f(x)=f(x^{\prime })$ implies that $x=x^{\prime }$ where A is the domain set of f and both x and x' are members of that set.

Horizontal Line Test
If no horizontal line intersects the graph of a function in more than one place then the function is a one-to-one function.