functional rules: 4 representations think of the following vending machine. how do you get each...
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Functional Rules: 4 Representations
• Think of the following vending machine. How do you get each item?1.
Functional Rules
As an In/Out Machine
Coke
$1.00
Chips
$1.25
Fruit
$0.75
Cookies
$0.75
PICK UP FOOD HERE
VENDING MACHINE PAY HERE
$1 $0.25
Functional Rules: 4 Representations
1. Functional Rules
As an In/Out Machine
Coke
$1.00
Chips
$1.25
Fruit
$0.75
Cookies
$0.75
PICK UP FOOD HERE
VENDING MACHINE
• The vending machine follows a rule:• Input: a certain amount of money• Rule: depending on money, give a type of
food or drink• Output: food or drink
Functional Rules: 4 Representations
• Functions are in/out machines
• Each input as only one output
• All have inputs and outputs
• The rule must always be followed
1. Functional Rules
As an In/Out Machine
MACHINE
FUNCTIONAL RULEINPUT OUTPUT
Functional Rules: 4 Representations
• Fill in the missing box:1. Functional Rules
As an In/Out Machine
RULE: # of interior angles
in shapeTriangle
RULE: First letter of the
monthJ
3 Angles
January orJune orJuly
RULE: Season of the
yearAugust Summer
Functional Rules: 4 Representations
• Domain: is the set of total possible input values. This is also the independent variable
• Range: is the set of total possible output values. This is also the dependent variable
FUNCTIONAL RULEINPUT
DOMAININDEPENDENT VAR.
OUTPUTRANGE
DEPENDENT VAR.
1. Functional Rules
As an In/Out Machine
Functional Rules: 4 Representations
• 4 Representations: Functions/Functional Rules can be represented in four ways:
• Graph• Data Table• Equation• Description of the Rule
FUNCTIONAL RULEINPUT
DOMAININDEPENDENT VAR.
OUTPUTRANGE
DEPENDENT VAR.
1. Functional Rules
As an In/Out Machine
GRAPH DATA TABLE EQUATION DESCRIBE RULE
4 REPRESENTATIONS
Functional Rules: 4 Representations
Describe the functional rule for the following in/out data tables. Write an equation if possible.
• I DO
2. Examples
In (x) Out (y)
10 23
5 13
1 5
0 3
Description: Output is two times the input, then add three
Equation: y = 2x + 3
Functional Rules: 4 RepresentationsDescribe the functional rule for the following in/out
data tables. Write an equation if possible.• WE DO
2. Examples
In (x) Out (y)
2 4
3 6
11 22
27
18
Description: Output is two times the input
Equation: y = 2x
54
9
Y = 2x
Y = 2(27) = 54
Y = 2x
18 = 2x
9 = x
Functional Rules: 4 Representations• YOU DO
2. Examples
In (x) Out (y)
2 7
4 13
7 22
10 31
12
76
Description:
Equation:
Rule: Output is three times the input, plus one
Y = 3x + 1
37
25
Y = 3x + 1
Y = 3(12) + 1 = 37
Y = 3x + 1
76 = 3x + 1
75 = 3x
25 = x
Functional Rules: 4 Representations• YOU DO
2. Examples
In (x) Out (y)
House 4
Cup 2
Writer 5
Elephant 7
Spin
Mathematics
Description:
Equation:
Functional Rules: 4 Representations1. Write at least 5 different rules for the following
in/out table
2. Create your own functional rule• You must have domain, range, rule and a
in/out table• Examples: McD Menu, Temperature
3. Classwork
In (x) Out (y)
10 30
RULE: Based on menu choice,
customer will pay output
INPUTValue Meal Choice
OUTPUTMoney owed
In (x) Out (y)
Big Mac $5.99
Nuggets $5.59
Qtr Pdr $5.25REMEMBER: EACH INPUT HAS ONLY ONE OUTPUT
Functional Rules: 4 Representations1. Using complete sentences, write a word splash
(short paragraph) explaining how you remember the following key terms are connected:
3. Classwork
(Finish rest for HW) Function Input Output
Rule Domain Range
Coordinate Plane Data Table Equation
Independent Variable
Dependent Variable
Four Representations