Examples of mathematical functions include y = x + 2, f(x) = 2x, and y = 3x - 5. Any mathematical statement that relates an input to one output is a mathematical function. Many simple mathematical functions are written as "f(x) = ..." where "f(x)" is spoken as "f of x," an abbreviated way of saying "function of x."
A mathematical function is a well-behaved mathematical relationship, meaning that it relates exactly one output to one input, as opposed to other mathematical relationships that relate multiple outputs to an input or to more than one input. For example, consider the function f(x) = 2x, which relates the input x with the output f(x). For every number assigned to the input x, an output f(x) is generated, which in the case of this function is equal to exactly two times the input. The possible set of numbers assignable to the input x is called the domain, while the possible set of numbers the function can generate is called the range.
In other words, in the mathematical function f(x) = 2x, over the domain of x the range of f(x) is equal to 2 times x. For the mathematical function y = 3x - 5, the range of y is equal to 3 times x minus 5 over the domain of x.