Introduction to Functions

What is a Function?

A function is a relation where each input has exactly one output.

Function Notation

$f(x) = 2x + 3$

• $f$ is the function name
• $x$ is the input
• $2x + 3$ is the rule

Evaluating Functions

To find $f(5)$ when $f(x) = 2x + 3$: $f(5) = 2(5) + 3 = 13$

Domain and Range

• Domain: Set of all possible input values
• Range: Set of all possible output values

Vertical Line Test

A graph represents a function if any vertical line intersects it at most once.