1. FUNCTIONS Vocabulary: Relation Function Domain Range
Independent Variable
Dependent Variable
Input values
Output values
Discrete
Continuous

2. The set of all first coordinates of a relation
This is read as the set f of ordered pairs.
The set of all first coordinates of a relation
is called the domain of the relation.
For f = { (1, 7), (2, 14), (3, 21), (4, 28) },
The domain is {1, 2, 3, 4}.
The set of all second coordinates
is called the range.
For f = { (1, 7), (2, 14), (3, 21), (4, 28) },
The range is {7, 14, 21, 28}.

3. This relation relates y to x; f relates y to x.
For f = { (1, 7), (2, 14), (3, 21), (4, 28) }.
Is it a FUNction??
We say that y depends upon the value of x.
So, y is called the dependent variable and
x is called the independent variable.
x is also called the input value and
y is called the output value.

4. What we’ve learned so far…x
y OR f(x)
Domain
Range
Independent variable
Dependent variable
Input values
Output values

5. Find the domain and range of the following relations, afterwards note
whether each IS or IS NOT a function.
1) { (2, 9), (5, 9), (8, 9), (11, 9) }
2) { (4, 5), (8, 1), (-2, 0), (4, 13) }
3) { (1, 5), (2, 5), (3, 5), (4, 5) }
4) { (-10, 5), (-6, 3), (-1, 0), (3, 5) }

6. Sometimes a relation can be represented by a graph.
A graph that contains only points is called discrete.
A graph that contains lines/curves is called continuous.
You can easily determine the domain and
range of a relation given a discrete graph. y
First, write the coordinates for each point. B
A ( -2, 4)
So the domain is
(all the x-values): C A
B ( 0, 8)
D = { -2, 0, 3, -4 }
C ( 3, 5)
And the range is
(all the y-values): x
D ( 3, -2) E D
E ( -4, 0)
R = { 4, 8, 5, -2, 0 }

7. Sometimes a relation can be represented by a table of values.x y 2 5 4 -6 3 6 8
The relation
f = { (2, 5), (4, -6), (3, 6), (2, 8) }
can be written as
a table of values.
H O R I Z O N T A L x 2 4 3 y 5 -6 6 8
Remember, the x-values represent domain values
of the relation and the y-values represent range values.

8. Sometimes a relation can be represented in a diagram called a mapping.
The relation
f = { (2, 5), (3, 7), (4, 9), (5, 11) }
is being diagramed in
mapping below.
The arrows in a mapping
relate y to x.
This is just another way to
represent ordered pairs:
(2, 5), (3, 7), (4, 9), (5, 11). x y 2 3 4 5 5 7 9 11
Remember:
Domain  x-values
Range  y-values

9. and range of the following relations
Name_________________________
Find the domain
and range of the following relations
Label each as function or not a function. 1)
{ (1,1), (2,2), (3,3), (4,4) } 2) 3) 4) 5) 6)
{ (2,1), (4,8), (0,6), (0,9) } 7) 8) 8 7 6 5 1 2 3 x y 3 -1 4 5 1 6 2 1 3 7 -8 -2 9 x 3 1 -3 y 5 8 -1