Definition of Function
Definition of Function
Summary
A function is defined as follows:
Definition
A function \(f\) consists of a set of inputs, a set of outputs, and a rule for assigning each input to exactly one output. The set of inputs is called the domain of the function. The set of outputs is called the range of the function.
Typically, a function is represented using one or more of the following tools:
- A table
- A graph
- A formula
We can identify a function in each form, but we can also use them together. For instance, we can plot on a graph the values from a table or create a table from a formula.
One can use the Vertical Line Test to determine if the graph represents a function. In this case, if there is a vertical line that intersects a set of points more than once, then the set of points does not represent a function.
\(Fig. 1\) (a) The set of plotted points represents the graph of a function because every vertical line intersects the set of points, at most, once. (b) The set of plotted points does not represent the graph of a function because some vertical lines intersect the set of points more than once.
For more information, refer to page 13 of the Calculus OpenStax book.