1. What’s my rule? 3
Input
(x)
output(y) ? 5 1 6 2 7 3

2. Today, we are going to learn how to generalize a variety of patterns to a symbolic rule from tables, graphs, or words ~ SPI

3. You are going to make some notations in your journals.
Snoopy’s
Journal

4. My Function Machine takes a value called input and performs one or more operations on it according to a “rule” to produce a new value called the output.

5. A function is a relation that assigns exactly one output value to one input value
output(y) 1 2
You can organize the input-output values of a function in a function table. 5 6 7 3 8

6. The function rule describes the relationship between each input and output.
(x)
output(y) 1 2 5 6
Add 5 7 3 8

7. I can use an algebraic expression to represent the rule of my function machine5
X + 5

8. You can also use a “rule” to describe a pattern in a sequence of numbers. For example: 8, 16, 24, 32, … A sequence is a list of numbers in a specific order. What rule would you use for the above sequence? +8

9. Add 8
Each number in a list is called a term of the sequence. An Arithmetic sequence can be found by adding the same number to the previous term. 8, 16, 24, 32, … +8 +8 +8

10. Times 5
In a Geometric Sequence, each term is found by multiplying the previous term by the same number. For example: 2, 10, 50, 250, …
x 5
x 5
x 5

11. You can also write an algebraic expression to describe a sequence
You can also write an algebraic expression to describe a sequence. The value of each term can be described as a function of its position in the sequence.
X + 5

12. You can show a sequence in a table
You can show a sequence in a table. The position of the number in the sequence is “x” and the value of each term is “y”
Position (x) 1 2 3 4
Value (y) 5 7 9 11
Notice the value increases by 2, so the first part of the rule would be 2x

13. If the rule were simply 2x, then the value for position 1 would be 2, but its 3 more. That means you add 3 to 2x to get the next term in the sequence.
Position 1 2 3 4
Value 5 7 9 11
Let’s check the rule 2x + 3!
2(1) + 3 = 5; 2(2) + 3 = 7 Yes!

14. What is the expression for the sequence in the table below?
Position 1 2 3 4
Value 9 14 ?
The value goes up by 5, so its 5x. But the next term is 1 less, so the expression is 5x – 1!

15. Who uses patterns and functions?

16. Functions are used in business to show costs
Functions are used in business to show costs. For example: Snoopytronics Inc. needs to hire a company to monitor employee computer activity. The cost is $4 for each computer.

17. Hmmm, I wonder what the rule would be…
If we make a table of input and output values of cost per computer, it would look like this:
Input
(x)
output(y) 1 2 3 4
Hmmm, I wonder what the rule would be… 4 8 12 16

18. The rule can also be written as an algebraic equation, such as y = 4x, where y is a function of x.

19. We can make a graph of this “rule” by using the x and y as coordinates.
y = 4x
Input
(x)
output(y) 1 2 3 4 16 12 8
Input
(x)
output(y) 1 2 3 4 16 12 8 4

20. Let c = the number of CD’s burned and
Suppose Snoop’s band recorded a CD. They want to make copies and sell them. They found a recording company that charges $250 for making a master CD and designing the art for the cover. In addition, they charge $3 to burn each CD. The total cost of making CD’s depends on the number of CD’s burned.
Let c = the number of CD’s burned and
t = the total cost. What would be the rule?

21. Yes! The rule would be…
t = 3c + 250

22. You can also write a rule from a graph using the coordinates!
Input
(x)
output(y) -1 1 2 3 5
Hint: make a table!
Y = 2x-1

23. Now, let’s try some examples!

24. What is the rule for the table below?
Correct! 5x

25. Which equation fits the table?
y = x + 15
y = 10x + 5
y = 3x + 12
y = 15x

26. What’s the rule for this one?
Correct!
Divide by 2,
or y = 1/2 x

27. What is the rule for the sequence in the table below?
Position (x) 1 2 3 4
Value (y) 13 21 29 37
Correct! 8x + 5

28. What would be the value for y if x = 4?
input(x)
output(y) 1 2 3 7 9 11
X = 15 13

29. See if you can guess the rule.
Correct! y = 4x + 1
input(x)
output(y) ? 1 2 3 1 5 9 13

30. I’ll give you a hint ~ make a table!
Can you guess the rule?
I’ll give you a hint ~ make a table!
input(x)
output(y) 1  0 2  2 3  4 4  ?

31. I need to workout.
Snoopy is thinking of joining a health club. It charges a one-time membership fee of $30 plus a monthly fee of $12. Write a rule for the total charge (y) for the number of months (x) Snoopy goes.
Correct! y = 12x + 30

32. Now, it’s your turn to create a real-world problem with a rule, a matching function table, and a coordinate graph of the rule. Write it in your journal.