Lesson 2: Function Notation
Part A: Introduction
Recall:
A function is a relation in which there is a unique output for each input.
Each value of the independent variable (the domain) must correspond
to only one value of the dependent variable (the range).
Example: Which of the following relations represents a function?
D = { Mississauga phone numbers }
R = { Mississauga residences/businesses }
INPUT:
(905) 824 – 1025
Function?
OUTPUT:
D = { eye colours }
R = { names of people in class }
INPUT:
brown
Function?
OUTPUT:
Part B: Definitions
Consider the relation y  2x  1 ,
x-y notation
vs
y  2x  1
 y  f (x )
function notation
f (x )  2x  1
 “f “ names a function
 f (x ) is another name for y
 Read as: “the value of f at x”,
or “ f of x “.
Symbols such as f (x ), g (x ), or h (x ) etc. are called function notation. They are
used to represent the value of the dependent variable y for a given value of the
independent variable x
INPUT
DOMAIN
OUTPUT
f(x)
RANGE
Part C: Examples
Example  Given f (x )  5  2x , evaluate:
a) f (4)
b) f (3)
c) f (4  x )
(4 is the input, what is the output?)
d) f (3)  f (8)
e) f (x )  6
(6 is the output, what is the input?)
Example  Given g (x )  x 2  2x  3 , evaluate:
a) g (2)
b) g (4a )
c) g (x )  0
d) g (x )  5
Example  The cost of a basic pizza is $10 and each additional topping is $1.50.
a) Use function notation to write an equation for the total cost of a
pizza.
b) Determine the cost when 3 toppings are selected.
c) If a pizza costs $22.00, how many toppings were added on.
Homework: p. 22 #1ace, 3, 5, 6, 7, 11, 12, 16, 17