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Input (x). output(y). What’s my rule?. 3. ?. 0. 5. 1. 6. 2. 7. 3. 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.

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Input (x)

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Input

(x)

output(y)

What’s my rule?

3

?

0

5

1

6

2

7

3

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 inputand performs one or more operations on it according to a “rule” to produce a new value called the output.

Input

(x)

output(y)

1

2

### A function is a relation that assigns exactly one output value to one input value

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

0

5

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3

8

Input

(x)

output(y)

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2

0

5

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

0

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

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

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

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”

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.

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?

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.

Input

(x)

output(y)

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### If we make a table of input and output values of cost per computer, it would look like this:

Hmmm, I wonder what the rule would be…

4

8

12

16

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

Input

(x)

Input

(x)

output(y)

output(y)

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### We can make a graph of this “rule” by using the x and y as coordinates.

y = 4x

4

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

Input

(x)

output(y)

0

-1

1

1

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3

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### You can also write a rule from a graph using the coordinates!

Hint: make a table!

Y = 2x-1

Now, let’s try some examples!

What is the rule for the table below?

Correct! 5x

Which equation fits the table?

• y = x + 15

• y = 10x + 5

• y = 3x + 12

• 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?

Correct! 8x + 5

input(x)

output(y)

0

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3

What would be the value for y if x = 4?

7

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X = 15

13

input(x)

output(y)

?

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See if you can guess the rule.

Correct! y = 4x + 1

1

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13

input(x)

output(y)

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0

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4

?

Can you guess the rule?

I’ll give you a hint ~ make a table!

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.