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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

Alg1A 3.04 - Map Function

 


  • 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)

Alg1A 3.04 - Map Relation

 

  • 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

Alg1A 3.04 - Square Root Map


  • 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) = _____.

Alg1A 3.04 - Map 01

Answer:  31

Because the input (domain) of July points to the output (range) of 31 days


  • Example
    • What is the function (notice the pattern)?

Alg1A 3.04 - Map 02

Answer: F(x) = x + 3

Because each input (x-value) is increased by 3 to result in the range (y-value)


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