Basics of Functions and Their Graphs
A
relation
is any set of ordered pairs.
(ex:
(
29
(
29
(
29
(
29
{
}
h
g
f
e
d
c
b
a
,
,
,
,
,
,
,
)
- The set of all first components of the ordered pairs is called the
domain
of the
relation.
(domain of the example relation = {a, c, e, g}
- The set of all second components is called the
range
of the relation.
(range of
the example relation = {b, d, f, h})
EX 1:
Find the domain and range of the relation:
(
29
(
29
(
29
(
29
(
29
{
}
8
.
21
,
25
,
7
.
20
,
20
,
9
.
18
,
15
,
2
.
16
,
10
,
8
.
12
,
5
Functions
A
function
is a relation in which each member of the domain corresponds to exactly one member of the range.
-No two ordered pairs have the same first component with different second components.
(note: a function can have two different first components with the same second component)
Examples:
EX 2:
Determine whether each relation is a function.
a.) { (1,2), (3,4), (5,6), (5,8) }
b.) { (1,2), (3,4), (6,5), (8,5) }
Functions as Equations
·Functions are usually given in terms of equations rather than as sets of ordered pairs.
ex. y = -0.016x
2
+ 0.93x + 8.5 – for each value of x, there is one and only one value of y
· x is the independent variable
· y is the dependent variable
*To determine whether an equation represents a function:
Solve for the dependent variable.
If you put one value in for the independent value and only get one
dependent value, the equation represents a function.
EX 3: