# 3.2 – Function Notation

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.”
• Make the letter outside the parentheses a capital letter and the letter inside the parentheses a lowercase letter
• Capitol(lowercase)
• Dependent(independent)
• A(d)

• 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
• 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)