Download explicit rules: input-output formulas

EXPLICIT RULES:
INPUT-OUTPUT
FORMULAS
Function Machine Model
1. If you input 4 into the function machine, the output is 6.
If you input 5 into the function machine, then the output is 7
What is the input-output rule for the function machine?
OUTPUT = INPUT + 2
___________________________________________
10
Therefore, if the input is 8 the output would be __________
2. If the input is 1, the output is 4.
If the input is 2, the output is 7.
If the input is 3, the output is 10.
What is the input-output rule for the function machine?
OUTPUT = INPUT + 3
_____________
When looking at a sequence, an INPUTOUTPUT formula connects the term number
to the term, rather than connecting the term
to the previous term like
NOW-NEXT formulas.
+4
INPUT-OUTPUT
FORMULA
OUTPUT = INPUT + 4
x +4
1 +4
2 +4
3
4
y
5
6
7
8
NOW-NEXT
FORMULA
+1
+1
+1
Start = 5
NEXT = NOW + 1
Examples
x
1
2
3
4
y
-2
-1
0
1
INPUT-OUTPUT:
OUTPUT = INPUT - 3
NOW-NEXT:
Start = -2
NEXT = NOW + 1
x
1
2
3
4
y
3
6
9
12
INPUT-OUTPUT:
OUTPUT = INPUT(3)
NOW-NEXT:
Start = 3
NEXT = NOW + 3
You Try!
x
2
3
4
5
y
1
1.5
2
2.5
x
1
2
3
4
y
3
5
7
9
NOW-NEXT:
NOW-NEXT:
x
1
2
3
4
y
1
8
15
22
NOW-NEXT:
Start = 1
Start = 3
Start = 1
NEXT = NOW + 0.5
NEXT = NOW + 2
NEXT = NOW + 7
INPUT-OUTPUT:
OUTPUT = INPUT(0.5)
INPUT-OUTPUT:
OUTPUT = INPUT(2) + 1
INPUT-OUTPUT:
OUTPUT = INPUT(7) - 6
What similarities do you see between the Now-Next rule and the Input-Output rule?
Repetitive addition can be written as multiplication  resulting in the
coefficient in the input-output rule
Then adjust with
addition/subtraction.
Comparing Rules
Complete with your table
Comparing Rules
Comparing Rules
Complete with your table
Comparing Rules
Comparing Rules
Input-Output Machines
-8
-8
+12
+12
Find the change in both the x column and the y column.
The rate of change is the change in y over the change in x
−8
−8
12
12
Both rates simplify to 1 so the coefficient is 1, then find the “adjustment factor” by
figuring out what you add or subtract to get to the y value.
𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑖𝑛𝑝𝑢𝑡 − 5
Input-Output Machines
-9
-3
-6
-2
Find the change in both the x column and the y column.
The rate of change is the change in y over the change in x
1
1
−3
−9
−2
−6
Both rates simplify to so the coefficient is , then find the “adjustment factor” by
3
3
figuring out what you add or subtract to get to the y value.
1
𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑖𝑛𝑝𝑢𝑡
3
Input-Output Machines
-3
+12
+6
-24
Find the change in both the x column and the y column.
The rate of change is the change in y over the change in x
12
−3
−24
6
Both rates simplify to -4 so the coefficient is-4, then find the “adjustment factor” by
figuring out what you add or subtract to get to the y value.
𝑜𝑢𝑡𝑝𝑢𝑡 = −4𝑖𝑛𝑝𝑢𝑡
Input-Output Machines
Work on your own to find the rest!