Transcript Function Notation & Evaluating Functions

FUNCTION NOTATION AND EVALUATING FUNCTIONS
SECTIONS 5.1 & 14.1B
relation is a set of __________________.
ordered pairs
A ________
The ________
of ________
numbers
domain is the ______
set
first
in a relation.
The ________
is the ______
of ________
range
set
second numbers
in a relation.
function
A ___________
is a relation in which no number in the
domain
repeated
_________
is __________.
Functions can be represented five different ways:
mapping
1. ______________
graph
2. ______________
3. ______________
table
Set of ordered pairs
4. ______________
equation
5. ______________
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
2 x  y  9.
a. ( 1, ? )
x 1
y if _________?
What is ____
2x  y  9
2 1  y  9
2  y  9 -2
y7
(1, 7)
b. ( ?, 9 )
x
y9
What is ____ if _________?
2x  y  9
2 x  9  9 -9
2x  0
2 2
x0
(0, 9)
TRY THIS….
c. ( 4, ? )
y if _________?
What is ____
x4
2x  y  9
2  4  y  9
8  y  9 -8
y 1
(4, 1)
Function notation replaces the independent 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 “ ____
Instead of writing,
y  x3
, we replace the y with
f ( x)
f ( x)  x  3
f of x equals x  3
is read as “ ___________________________________”
Function
Notation
f ( x)  x
Read as
2
2
f of x equals x
f ( x)  x
f of x equals the absolute value of x
f of x equals the square root of x
f ( x)  x
2
f ( x)  3  x2
f of x equals 3  x
Look at the mappings below.
is happening
to
What is happening to each number in theWhat
domain
to get the
x to get the
corresponding number in the range?
Domain
Range
2
8
5
11
10
16
x
Domain
x
f ( x)
Range
f ( x)
-3
-6
0
0
5
10
corresponding f(x)
value?
Function Rule:
f ( x)  x  6
What is happening to
x to get the
corresponding f(x)
value?
Function Rule:
f ( x)  2 x
function rule can be thought of as an operation that changes the
The ______________
numbers in the ___________
to make the ________.
domain
range
f ( x)  3x2  4 x  2
Function notation:
function rule
The right side of any function notation is called the _____________.
Replace
the y with
f(x)
Right side
of notation
Equation
Function Notation
Function Rule
y  x6
f ( x)  x  6
x6
y  2 x2  3
f ( x)  2 x2  3
2x  3
y  4 x 7
f ( x)  4 x  7
4 x 7
2
input
The numbers of the domain are sometimes called the ________
and the
output
range is called the ___________.
Changes the domain
into the range
x
input
output
Function Rule
f ( x)
Find the range for the function
f ( x)  3x  1
if the domain of f(x) is { 0, 2, 4 }.
domain
Range = { 1, 7, 13
3x  1
range
Domain
0
3  0  1
1
2
3  2  1
Range
0
1
2
7
4
13
7
4
3  4  1
}
Written as ordered pairs:
13
{(0,1),(2,7),(4,13)}
Try this…
h( x)  x  2
2
For the function,
, find the range
if the domain is { -3, 0, 4 }.
x2  2
Input
3
 3
0
0
4
 4
Output
2
=
92
7
2
2
=
02
2
2
2
=
16  2
14
2
Range: {2, 7, 14}
Sometimes we only want to only evaluate one element of the domain.
For example, if
“find
g ( x)  x2  3x  1 find g ( x) when
x2
g ( x) when x  2 ”, can be written in a shorter form as “ g (2) ”.
Example 2: If g ( x)  x  3x  1 find
2
g (2)
g ( x)  x 2  3x  1
g ( 2) .  2   3  2   1
2
Plug 2 into
the
function
rule.
g (2)  4  6  1
g (2)  1
g (2)  1
If h( x)  2 x  3x  2
2
Try these…
find:
A. h(0)
h ( 0)  2  0   3  0   2
.
2
h(0)  0  0  2
h(0)  2
B. h(2)
h ( 2)  2  2   3  2   2
.
2
h(2)  2  4  6  2
h(2)  8  6  2
h(2)  0