# 3.4 – Domain & Range

Objectives

• Define mapping diagram.
• Given a mapping diagram, map inputs to outputs.
• Determine whether a mapping diagram represents a function.
• Define domain and range.
• Given a mapping diagram, identify elements of the domain and range.

Key Terms

• Mapping – A specified way of connecting inputs to outputs.
• If each input is mapped to only ONE output, the mapping is called a function.
• A mapping can also be called a relation.
• Mapping Diagram – A diagram that shows how a specific relation maps input values to output values.
• Relation – Any set of input and output values.
• In a relation, a single input gives back one or more outputs.

Notes

• All functions are relations.
• Some relations are functions.
• Only if each input is paired with exactly ONE output.

• Function Map
• This is a function because each input (left) is paired with exactly one output (right)
• Domain: {1, 2, 3, 4}
• Range: {1, 2, 3}
• Points: (1,2), (2,1), (3,1), (4,3)
• Note: Each input points to exactly one output

• Relation Map
• This is a relation because some inputs (left) are paired with more than one output (right)
• Domain: {1, 2, 3, 4}
• Range: {1, 2, 3, 4}
• Points: (1,1), (2,2), (2,3), (3,4), (4,3)
• Note: The input of 2 points to two different outputs (2 and 3)

• Another Relation Map
• Domain: {1, 4, 9}
• Range: {-3, -2, -1, 1, 2, 3}
• Points: (1,-1), (1,1), (4,-2), (4,2), (9,-3), (9,3)
• Note: Each input points to more than one output

• Inputs and Outputs
• Outputs are a function of inputs
• Outputs depend on inputs
• Notation:  OUTPUT(input) = O(i)

• In function notation, F(x) is the output, so F(x) is the same as y.
• F(x) is the result of a function
• The result of a function is the output, which is the y-value
• So,  F(x) = y
• In algebra, a relationship where one quantity depends on another quantity is called a function.
• A set of input and output values where each input value has one or more output values is called a relation.

• Example
• Given the mapping diagram, DAYS(month), below, DAYS(July) = _____.