MCR3U1
U2L2
FUNCTION NOTATION
(Introduction to Functions)
PART A ~ 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 
a)
Which of the following relations represents a function?
D = { Mississauga phone numbers }
R = { Mississauga residences/businesses }
INPUT:
(905)824–1025
FUNCTION?
OUTPUT:
b)
D = { eye colours }
R = { names of people in class }
INPUT:
brown
FUNCTION?
OUTPUT:
PART B ~ FUNCTION NOTATION
An equation that is a function can be named using function notation.
x–y notation
function notation
y = 3x + 5
f(x) = 3x + 5
Notice that the symbol f(x) is another name for y.
It is 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). For this reason, y and f(x) are interchangeable!
DOMAIN
INPUT
INPUT
f(x)
OUTPUT
INPUT
RANGE
MCR3U1
U2L2
PART C ~ EXAMPLES
Example 
a)
g(3) =
b)
g(–1) =
c)
x if g(x) = 1
Example 
a)
Determine each value from the given graph:
Given f(x) = 5 – 2x, determine:
f(4)
b)
f(–3)
c)
f(½)
e)
f(3) – f(8)
f)
x if f(x) = 6
(The input is 4, what is the output?)
d)
f(4 – x)
(The output is 6, what is the input?)
Example 
Given g(x) = x2 + 2x – 3, determine:
a)
g(2)
b)
g(4a)
c)
x if g(x) = 0
d)
x if g(x) = 5
MCR3U1
U2L2
Example 
Consider the functions f(x) = x2 – 3x and g(x) = 1 – 2x. Show that
f(2) > g(2) and explain what that means about their graphs.
Example 
The cost of a basic pizza at Guido’s Pizza is $10 with each
additional topping costing an extra $1.50.
a)
Use function notation to write an equation for the total cost of a pizza.
b)
Determine the cost of a pizza when 3 additional toppings are selected.
c)
If a pizza costs $22, determine how many additional toppings were added
to the pizza.
HOMEWORK: p.22–24 #1–7, 11, 12, 16, 17