Function

Definition

A function is a relation between a set of inputs and a set of permissible outputs where each input is related to exactly one output. It is often represented as $f(x)$.

5 Must Know Facts For Your Next Test

1. A function maps each element from its domain to exactly one element in its range.
2. The domain of a function is the complete set of possible input values.
3. The range of a function is the complete set of all possible resulting output values.
4. Functions can be represented using equations, tables, graphs, or verbal descriptions.
5. The vertical line test can be used to determine if a graph represents a function.

Review Questions

• What defines the relationship between inputs and outputs in a function?
• How do you identify the domain and range of a given function?
• What does the vertical line test help you determine?

Related terms

Domain: The set of all possible input values for which a function is defined.

Range: The set of all possible output values that result from using the inputs in the domain.

Function Notation: A way to denote functions in the form $f(x)$ where $x$ represents an input value.