Today you will:
Determine whether a relation
is a function
and
Use function notation and
find function values
1.7 Functions
A function is a relation in which each input has exactly one output
You can determine if a relation is a function by checking the table:
x
y
3
-4
-5
2
-7
-4
-5
7
You can determine if a relation is a function by
checking the mapping:
-7
-5
3
-4
2
7
You can determine if a relation is a function by looking at the graph:
A discrete function is a graph that consists of points
that are not connected.
(It does not make sense to connect the points
because there is no data between the points.)
Example:
The table below displays each student and their last test score.
Student:
Score:
1
88
2
95
3
87
4
78
A continuous function is a graph that consists of
points that are connected.
(It does make sense to connect the points because
there is data between the points.)
Example:
The table below displays a plant's height at various times.
Day:
0
Height (in.): 8
10
10
20
15
30
17
40
18.5
To review...
we know:
The input of a function is the
variable
.
The output of a function is the
variable
.
*The value of the dependent variable depends on, oris
a function of, the value of the independent variable.
Function Notation
If x is the independent variable and y is the dependent variable, then
we can write a function using function notation.
Function notation for y is f(x)
Function Notation uses the symbol f(x)
where f names the function
We say, " f of x"
*** It does not mean f times x !!!
The dependent variable is a function of the independent variable
.
y is a function of x
y
=
f (x)
Example:
Chris is buying several DVDs that cost $15 each
Dependent Variable : total cost
Independent Variable: number of DVDs purchased
We can write y = 15x
or f(x) = 15x
The total cost is a function of how many DVDs Chis buys.
Kay donates twice what Ed donates
Dependent Variable : Kay's donation
Independent Variable: Ed's donation
y = 2x
f(e) = 2e
So,
donation is a function of
donation.
If
Find
f(3)
Find
f(8)
f(x) = 15x
If
g(x) = 2x - 3
Find g(-2) + g(4)
Find g(w)
Find g(w+5)
Find g(w) +5