1. FUNCTION NOTATION AND EVALUATING FUNCTIONS

2. A ________ is a set of __________________.
relation
ordered pairs
The ________ is the ______ of ________ numbers in a relation.
domain
set
first
The ________ is the ______ of ________ numbers in a relation.
range
set
second

3. Functions can be represented five different ways:
A ___________ is a relation in which no number in the
_________ is __________.
function
domain
repeated
Functions can be represented five different ways:
1. ______________
2. ______________
3. ______________
4. ______________
5. ______________
mapping
graph
table
Set of ordered pairs
equation

4. Sometimes we will only know one part of the ordered pair
Sometimes we will only know one part of the ordered pair. We can use the equation to find the missing number.
Example 1:
Complete each ordered pair so that it is a solution to
a. ( 1, ? )
What is ____ if _________?
(1, 7) -2

5. b. ( ?, 9 )
What is ____ if _________?
(0, 9) -9

6. TRY THIS….
c. ( 4, ? )
What is ____ if _________?
(4, 1) -8

7. Does not mean multiplication!
Function notation replaces the dependent variable, y with either f(x), g(x), or h(x). f of x
f(x) is read as “ ____ _____ _____”
Does not mean multiplication! g of x
g(x) is read as “ ____ _____ _____” h of x
h(x) is read as “ ____ _____ _____”

8. Instead of writing, , we replace the y with Function Notation Read as
is read as “ ___________________________________”
Function Notation
Read as

9. Look at the mappings below.
What is happening to each number in the domain to get the corresponding number in the range?
What is happening to x to get the corresponding f(x) value?
Domain Range 8 11 16 2 5 10
Function Rule:
What is happening to x to get the corresponding f(x) value?
Domain Range -6 10 -3 5
Function Rule:

10. Replace the y with f(x) Right side of notation
function rule
The ______________ can be thought of as an operation that changes the
numbers in the ___________ to make the ________.
domain
range
Function notation:
The right side of any function notation is called the _____________.
function rule
Replace the y with f(x)
Right side of notation
Equation
Function Notation
Function Rule

11. Changes the domain into the range
The numbers of the domain are sometimes called the ________ and the range is called the ___________.
input
output
Changes the domain into the range
input
output
Function Rule

12. Find the range for the function
if the domain of f(x) is { 0, 2, 4 }.
range
domain
Range = { }
Domain
Range 2 4 1 7 13
Written as ordered pairs:

13. Range: Try this… For the function, , find the range
if the domain is { -3, 0, 4 }.
Input
Output = = =
Range:

14. Plug 2 into the function rule.
Sometimes we only want to only evaluate one element of the domain.
For example, if
find
when
“find
when
”, can be written in a shorter form as “ ”.
Plug 2 into the function rule.
Example 2: If
find .

15. Try these… If
find: A. . B. .

16. Functional Notation
An equation that is a function may be expressed using functional notation.
The notation f(x) (read “f of (x)”) represents the variable y.

17. Functional Notation Cont’d
Example:
y = 2x + 6 can be written as f(x) = 2x + 6.
Given the equation y = 2x + 6, evaluate when x = 3.
y = 2(3) + 6
y = 12

18. Functional Notation Con’t
For the function f(x) = 2x + 6, the notation f(3)
means that the variable x is replaced with the
value of 3.
f(x) = 2x + 6
f(3) = 2(3) + 6
f(3) = 12

19. Evaluating Functions Given f(x) = 4x + 8, find each: f(2) 2. f(a +1)
= 4(2) + 8
= 16
= 4(a + 1) + 8
= 4a
= 4a + 12
= 4(-4a) + 8
= -16a+ 8

21. Determine the value of x when given f(x).
Given f(x) = 4x + 8, determine x when:
f(x) = 2
f (x) = -1

23. Evaluating More Functions
If f(x) = 3x  1, and g(x) = 5x + 3, find each:
f(2) + g(3)
= [3(2) -1] + [5(3) + 3] =
= 23
f(4) - g(-2)
= [3(4) - 1] - [5(-2) + 3]
= (-7)
= 18
f(1) + 2g(2)
= 3[3(1) - 1] + 2[5(2) + 3] =
= 32