Function Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Determine whether the relation {(1,3),(2,5),(3,7),(4,9)}\{(1, 3), (2, 5), (3, 7), (4, 9)\} is a function.

Solution

  1. 1
    A relation is a function if every input (first element) maps to exactly one output (second element).
  2. 2
    List the inputs: 1,2,3,41, 2, 3, 4. Each input appears exactly once, so each has a unique output.
  3. 3
    Since no input is repeated with a different output, this relation is a function.

Answer

Yes, it is a function.\text{Yes, it is a function.}
A function assigns exactly one output to each input. The vertical line test for graphs and the uniqueness of first elements in ordered pairs are equivalent ways to check this.

About Function

A function is a rule that assigns to each input in the domain exactly one output in the codomain — every input maps to precisely one output, never two.

Learn more about Function →

More Function Examples

Example 2 medium

Does the equation [formula] define [formula] as a function of [formula]?

Example 3 easy

Is the relation [formula] a function? Explain.

Example 4 hard

A graph passes through the points [formula], [formula], [formula], and [formula]. Does this graph re

Example 5 medium

Given [formula], find [formula] and determine if [formula] is a function.

← All Function Examples Function Concept