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. In mathematical notation, it is often represented as f(x).

5 Must Know Facts For Your Next Test

1. A function can be represented in various forms such as equation, graph, table, or mapping diagram.
2. The domain of a function is the complete set of possible values of the independent variable.
3. The range of a function is the complete set of all possible resulting values of the dependent variable.
4. A function passes the vertical line test if no vertical line intersects its graph more than once.
5. Common types of functions include linear, quadratic, polynomial, rational, and exponential functions.

Review Questions

• What are the different ways to represent a function?
• How do you determine if a relation is a function using the vertical line test?
• Explain the difference between the domain and range of a function.

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.

Inverse Function: A function that reverses another function; if f(x) = y then its inverse f^(-1)(y) = x.