Input(x)

output(y)

0 5

1 62 7

3?

3

What’s my

rule?

Today, we are going to learn

how to generalize a

variety of patterns to a symbolic rule from tables, graphs, or

words ~ SPI 706.1.2

You are going to

make some notations in

your journals.

Snoopy’s

Journal

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.

A function is a relation that

assigns exactly one output value

to one input valueYou can

organize the input-output values of a function in a function table.

Input(x)

output(y)

123

0 5678

The function rule describes the

relationship between each input and output.

Input(x)

output(y)

12

0 567

3 8

Add 5

I can use an algebraic expression to represent the rule of my function

machine0

5

X + 5

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

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

Add8

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

Times5

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

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

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!

What is the expression for the sequence in the

table below?Position 1 2 3 4

Value 4 9 14 ?

The value goes up by 5, so its 5x. But the next term is 1

less, so the expression is 5x –

1!

Who uses

patterns and

functions?

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.

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 16

4

8

12

Hmmm, I wonder

what the rule would be…

The rule can also be

written as an algebraic

equation, such as y = 4x, where y is a function

of x.

We can make a graph of this “rule” by using

the x and y as coordinates.

Input(x)

output(y)

1

2

3

4 16

12

8

4

y = 4xInput

(x)output(y)

1

2

3

4 16

12

8

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?

Yes! The rule

would be…

t = 3c + 250

You can also write a rule from a graph using

the coordinates!Input

(x)output(y)

0 -1

1 1

2 3

3 5

Y = 2x-1

Hint: make a table!

Now, let’s try

some exampl

es!

What is the rule for the table

below? Correct! 5x

Which equation fits

the table?

A. y = x + 15

B. y = 10x + 5

C. y = 3x + 12

D. y = 15x

What’s the rule for this

one? Correct!

Divide by 2,

or y = 1/2

x

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

What would be the value for y if x

= 4?

input(x)

output(y)

0  

1 

2 

3 

7

9

11

13 X = 15

input(x)

output(y)?

0  

1 

2 

3 

See if you can guess the rule.

1

5

9

13

Correct! y = 4x + 1

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  ?

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.

I need to workout.

Correct! y = 12x + 30

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.