**Objectives**

- Translate between English sentences and math functions.
- Use function notation to represent relationships of dependence.
- Identify the object being depended on in function notation.
- Write function notation for general relationships and specific values.
- Use variables to represent names of functions.

**Key Terms**

- Function notation – A type of writing that uses a letter to name a function and places parentheses around the independent variable.
- The notation F(x) is pronounced “F of x.”

- Function – A special type of relationship in algebra where two quantities are related to each other so that one quantity depends on (or is a function of) the other.

**Notes**

- Function Notation: Output(input)
- The name
*F(x)*means “*F*is a function of*x*.”- When read out loud, you would say “
*F*of*x*.”

- When read out loud, you would say “
- Make the letter outside the parentheses a capital letter and the letter inside the parentheses a lowercase letter
- Capitol(lowercase)
- Dependent(independent)
- A(d)

- The name

- Example
- How to say it – English: The radius of a circle with a circumference of 10 feet
- How to write it – Notation: R(10)

- Examples
- Volume(radius) = 67
- Temperature(20 minutes), Temperature(20), and T(20) all represent the temperature of a liquid after it is heated for 20 minutes

- How to say it:
- English: The radius of a circle with a circumference of 10 feet

- How to write it:
- Notation: R(10)

- Examples
- If Pay(hours) is the function that describes Al’s monthly pay at Happy Cat Labs, based on his training, Pay(22 hours), Pay(22), and P(22) all represent his Monthly pay with 22 hours of training
- Expressions that give the monthly pay of an employee with 42 hours of training: P(42) or Pay(42)
- A balloon rising at a constant rate will rise farther in 60 seconds than in 45 seconds.
- Height increase(60) > Height increase(45)

- The cost of 4 kilograms of cheese is 50 dollars: Cost(4) = 50
- The amount of time spent driving (which depends on the speed of the car) is 5 hours: Time(speed) = 5
- The height of an oak tree (which depends on the age of the tree) is 100 feet: Height(age) = 100
- The weight of a tiger (which depends on the age of the tiger): Weight(age)
- R(w) means: R is a function of w
- P is a function of x is written as: P(x)
- The efficiency of a car depends on the weight of the car: Efficiency(weight), or E(w)
- When you read V(r) aloud, you can shorten it to “V of r.”
- The postage required to mail a box depends on its weight: Postage(weight), or P(w)
- The value of a used car depends on its age: Value(age), or V(a)