**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.

- 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).

- The function F(y) takes a measurement in yards (as input) and returns a measurement in feet (as output).

- 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:

- Example: What is the value of S(13)?
- Set up the function:
- Solve:
- 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:

- Example: What is the value of A(3)?
- Set up the function:
- Solve:
- 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.