MCR3U1
U2L1
RELATIONS & FUNCTIONS
(Introduction to Functions)
PART A ~ DEFINITIONS
relation:
a relationship between two variables; values of the independent
variable are paired with values of the dependent variable
function:
a relation where each value of the independent variable corresponds
with only one value of the dependent variable
THE DOMAIN CANNOT REPEAT!
domain:
the set of all values of the independent variable of a relation
(the x–coordinates)
range:
the set of all values of the dependent variable of a relation
(the y–coordinates)
PART B ~ DESCRIBING A RELATION

Using WORDS.
ex.

LISTING the elements.

TABLE of VALUES
“Barney delivers flyers. He earns $25 per
day plus $10 per bundle of 100 flyers.”
ex.
ex.

GRAPHICALLY
{ (1,2), (3,4), (5,6), (7,8) }
x
y = 3x + 1
–1
–2
0
1
1
4
ex.
y
y
x
x
2
7
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
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MAPPING DIAGRAM
ex.
x
y
0
–4
–2
0
2
4
2
4

EQUATION
ex.
y = 2x – 5
y = (x + 5)2 + 2
(linear)
(quadratic)
PART C ~ EXAMPLES
Example 
State the domain and range for each of the following:
{ (1,3), (2,–4), (3,5), (4,5) }
x
y
5
2
D=
D=
R=
R=
Is it a function?
Is it a function?
5
4
5
6
y
x
4
5
x
6
D=
D=
R=
R=
Is it a function?
Is it a function?
y
–3
7
5
8
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U2L1
THE VERTICAL LINE TEST:
If each vertical line drawn intersects the graph of a relation
in at most one point, then the relation is a function.
Example 
Determine the domain and range using real numbers.
State whether or not the relation is a function.
y
y
y
x
x
x
D=
D=
D=
R=
R=
R=
Is it a function?
Is it a function?
Is it a function?
PART D ~ RELATIONS VS. FUNCTIONS
Example 
a)
Graph a relation in the given form:
linear ~ y = mx + b
b)
y
y
x
c)
quadratic ~ y = a(x – h)2 + k
circle ~ x2 + y2 = r2
y
x
x
MCR3U1
U2L1
Example 
Compare y = x2 to x = y2. Which relation is a function?
y = x2
x = y2
y
y
x
x
A relation is a function when substitution of a value of
the independent variable (x) into the equation results
in more than one value of the dependent variable (y)!
Example 
Determine which relations are functions:
a)
y = 5x – 3
b)
y = –3(x + 2)2 + 4
c)
y  x 3
d)
x + y2 = 4
HOMEWORK: p.10–12 #1–4, 6, 7, 9, 12