Function

Definition

A function is a relation between a set of inputs and a set of permissible outputs such that each input is related to exactly one output. Functions are often represented by $f(x)$ where $x$ is the input variable.

5 Must Know Facts For Your Next Test

1. A function can be defined using different types of expressions such as equations, tables, and graphs.
2. The domain of a function is the complete set of possible input values (x-values) that produce valid outputs.
3. The range of a function is the complete set of all possible resulting output values (y-values).
4. A function passes the vertical line test if no vertical line intersects its graph more than once.
5. Function notation $f(x)$ specifies that $f$ is a function with $x$ as its input variable.

Review Questions

• What does the vertical line test determine about a graph?
• How do you find the domain and range of a given function?
• What does $f(x)$ mean in terms of functions?

Related terms

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

Range: The set of all possible output values produced by a function.

Vertical Line Test: A method to determine whether a graph represents a function; if any vertical line crosses the graph more than once, it is not a function.