Functions

Rules that assign exactly one output to each input.

Function vs. not a function

Definition

A function is a rule that assigns exactly one output to each input. Think of it as a machine: you put a number in, you get a number out — always the same number for the same input.

We write $f(x)$ (read "f of x") for the output when the input is $x$ .

Domain: the set of allowed inputs
Range: the set of actual outputs

Evaluating a function

Let $f(x) = 2x + 3$ .

$f(4) = 2(4) + 3 = 11$

$f(-1) = 2(-1) + 3 = 1$

Evaluate the function

Let $g(x) = x^2 - 1$ . Find $g(3)$ .

Related concepts

Algebra· Linear Equations

Graphing LinesPlotting linear equations on the coordinate plane using slope and intercepts.

Algebra· Polynomials

Quadratic EquationsEquations involving a squared variable, solved by factoring or the quadratic formula.