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3.3 – Input-Output Machines

Objectives

  • Picture functions as “input-output machines”
  • Compare the values placed into a function with the notation returned from a function
  • Identify domains and ranges of functions
  • Map domains and ranges of functions with an input-output diagram
  • Apply a rule to an input-output diagram and function notation

 

Key Terms

  • Domain – The set of all possible input values of a function (x-values on a graph).
  • Input – A number that is entered into a function.
    • The x-value, input, independent variable, domain
  • Input-Output Diagram – A diagram that relates the inputs of a function to its outputs.
    • Input values are shown on the left, with arrows pointing to the output values on the right.
    • The values on the left belong to the function’s domain.
    • The values on the right belong to the function’s range.

Alg1A 3.03 - Function Machines

Alg1A 3.03 - Function Machines02

  • Output – The result of a function.
    • The y-value, output, dependent variable, range
  • Range – The set of all possible output values of a function (or y-values on a graph).

 

Notes

  • Odd Number Function:  O(n) = 2n – 1
  • Even Number Function:  E(n) = 2n

 

  • A yard is equal in length to three feet.
    • The function F(y) takes a measurement in yards (as input) and returns a measurement in feet (as output).
      • So, the x-value (input) is actually listed as “y” because “y” stands for “yards”
      • And, the y-value (output) is the answer in “feet”
    • Function for Yards to Feet: F(y) = 3y
      • Because, for every yard, you get 3 feet (so you have to multiply yards times 3 feet).

 

  • Example: F(15.4) = ? ft
    • Set up the function: F(15.4) = 3(15.4)
    • Solve: F(15.4) = 46.2 ft
    • 15.4 yards will produce 46.2 feet
    • The result, in feet, of 15.4 yards is 46.2 feet

 


  • S(n) is a function that squares numbers.
    • Function: S(n)=n^2

 

  • Example: What is the value of S(13)?
    • Set up the function: S(13)=13^2
    • Solve: S(13)=169
    • The square of a 13 results in the value 169
    • The result of squaring 13 is 169

 


  • A(r) is a function that gives the area of a circle with radius r.
    • Function: A(r) = 3.14r^2

 

  • Example: What is the value of A(3)?
    • Set up the function: A(3) = 3.14\bullet3^2
    • Solve: A(3) = 28.26
    • The area of a circle with a radius of 3 is 28.26 units squared.

 


  • Example of the Odd Number Function
    • Solve: O(n) = 2n – 1 for O(30)
    • Step 1: Substitute 30 for n: O(30) = 2(30) – 1  =  60 – 1  =  59
    • Step 2: Notice if this is an Odd or Even number. This is an odd number, so it is the 30th odd number.
  • Example of the Even Number Function
    • Solve:  E(n) = 2n for E(7)
    • Step 1: Substitute 7 for n:  E(7) = 2(7) = 14
    • Step 2: Notice if this an Odd or Even number.  This is an even number, so it is the 7th even number.

 

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