Transcript Functions - KCMS 8th Grade Math Class KCMS 8th Grade Math

Linear Functions
Day 1
(Module 17)
Warm Up
Pouring Peanuts
Definition
What is a Function?
Guided Practices
Is it a Functional Relationship?
The “Functional” MP3
Definitions
Function Notation
Domain and Range
Recap on Functions
Functions
• Create Frayer models for each of your
definitions. They do not need to be big.
Definitions
Functions
Domain
Range
Function Notation
Relations
There will be a
vocabulary Check
What is a Function?
(Definition)
A FUNCTION is a relationship
between input and output.
In a FUNCTION, the output
depends on the input.
You can write a “depends on” sentence to help examine a
FUNCTIONAL relationship.
Your pay isdepends
onof
a function
dependent
quantity
output
y
the hours worked.
independent
inputquantity
x
In a FUNCTION, there is exactly one output for each input.
Glencoe Algebra I, Page 58
Is it a Functional Relationship?
(Guided Practice)
Examine each set of data below. Determine if it represents a
functional relationship. Explain why or why not.
1
Grade you receive on a test and the number of problems
The grade you receive on a test is a function of (depends on) the
missed number of problems you missed. Therefore, this is a functional
relationship.
2
The amount of money you have and the amount of gas
you put in your car The amount of gas you put in your car is a function of
(depends on) the amount of money you have.
Therefore, this is a functional relationship.
3
Your height and the width of your waist
There is no relationship between your height and the width of your waist.
Therefore, this is NOT a functional relationship.
4
Your height and your age
Your height is a function of (depends on) your age. Therefore, this is a
functional relationship.
The “Functional” MP3
(Guided Practice)
Independent
Input
Process
Column
Dependent
Output
1
Rap
2
Country
3
Jazz
What happens when I press 4?
4
Latin
A Latin song will play
5
Classical
What happens when I press 2?
A Country song will play
Does this represent a function?
Yes
Apollo
If it represents a function, write
a “depends on” sentence.
The type of song played depends
on the number selected.
If it represents a function, write a
“function” sentence.
The type of song is a function of
the number selected.
1
The “Functional” MP3
(Guided Practice)
Remember that the
definition stated that in a
FUNCTION, there is
exactly one output for
each input.
Independent
Input
Process
Column
1
Rap
2
Country
3
Jazz
4
Latin
5
Classical
Apollo
Let’s examine the table to
determine if this is true.
There is exactly one type
of song (output) for each
assigned number (input).
Dependent
Output
1
The “Functional” MP3
(Guided Practice)
Does the table represent a
function?
Hint: Create a mapping.
1
Rap
2
Country
3
Jazz
4
Latin
5
Classical
Yes, this is a function.
Independent
Input
Process
Column
Dependent
Output
1
Rap
2
Country
3
Jazz
4
Latin
5
Classical
Apollo
1
The “Functional” MP3
(Guided Practice)
Does the table represent a
function?
Hint: Create a mapping.
3
1
5
4
2
Rap
Independent
x
Process
Column
1
Country
2
Classical
3
Rap
4
Latin
5
Rap
Apollo
Country
Latin
Classical
Yes, this is a function.
Dependent
y
2
The “Functional” MP3
(Guided Practice)
Does the table represent a
function?
Independent
x
Process
Column
3
Rap
1
Country
5
Rap
4
Latin
2
Classical
3
1
5
4
2
Rap
Apollo
Country
Latin
Classical
Yes, this is a function.
Dependent
y
3
The “Functional” MP3
(Guided Practice)
Does the table represent a
function?
3
Rap
1
Country
5
Latin
2
Classical
Independent
x
Process
Column
3
Rap
1
Country
5
Rap
1
Latin
2
Classical
Apollo
4
No, this is NOT a function.
If you press 1, which song
would play?
Dependent
y
The “Functional” MP3
(Guided Practice)
Does the table represent a
function?
1
Independent
x
Process
Column
1
Rap
2
Rap
3
Rap
4
Rap
5
Rap
2
3
Apollo
Rap
4
5
Yes, this is a function.
There is exactly one
output for each input.
Dependent
y
5
Assignment
• Complete Apollo Chill
assignment. Put it in your
interactive notebook and get
it checked by Mrs. Sims.
Then start on the next slide
Function Notation
(Definition)
Equations that are functions can be written in a
function notation.
form called
For example, instead of writing an equation as
y = 3x – 8, you can replace the y with f(x).
Equation Notation
y = 3x – 8
Function Notation
f(x)
So, how do we read “f(x)”? Although it looks like
we would read it as “f times x” or “f parentheses x”,
we read it as “f of x”.
Read f(x) = 3x – 8 as “f of x equals 3x minus 8”.
Function Notation
(Definition)
In a function, x represents the independent quantity,
input, or the elements of the domain.
f(x) represents y, the dependent quantity, output, or
the elements of the range.
For example, f(5), is the element in the range that
corresponds to the element 5 in the domain.
We say that f(5) is
the function value
of f for x = 5.
Glencoe Algebra I, Page 148
Function Notation
f(x) = 3x – 8
f(5) = 3(5) – 8
f(5) = 7
Function Notation
(Definition)
Not only can you use substitution to evaluate functions,
you can examine the table and graph of the function.
Substitution
f(x) = –2x – 8
f(–1) = –2 (–1) – 8
f(–1) = –6
Graph
f(x) = – 2x – 8
Table
x
–3
f(x)
–2
–4
–1
–6
–2
( –1, – 6)
Function Notation
(Definition)
Let’s take a look at the function f(x) = 2x – 4 to further examine
function notation as it connects to multiple representations.
This function can be modeled by the relation {(2, 0), (3,2), (5,6),
(6,8)}. Remember, a relation is simply a set of ordered pairs.
Use the table feature of your calculator to verify the relation.
2
0
3
2
5
6
6
8
x
f(5) = 6
f(x)
2
0
3
2
5
6
6
8
Range
y
Domain
x
Dependent
Independent
f(x) = {(2,0) (3,2) (5,6) (6,8)}
Domain and Range
(Definition)
The set of the first numbers of the ordered pairs is the domain.
The set of second numbers of the ordered pairs is the range.
f(x) = {(1,15) (2,16) (3,17) (4,18) (5,19)}
Does this relation
and mapping
represent a function?
YES
1
15
2
16
3
17
4
18
5
19
Explain.
Each input value
is assigned to
exactly one
output value.
Domain and Range
(Definition)
The domain and range can also be written as a relation.
f(x) = {(1,15) (2,16) (3,17) (4,18) (5,19)}
Domain = { 1, 2, 3, 4, 5}
Range = { 15, 16, 17, 18, 19}
Notice that the first elements in each ordered pair is part of the
domain.
The second elements in each ordered pair is part of the
range.
Create A chart
• Create a chart that describes X and Y
X
Y
THE END