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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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slide1

Input

(x)

output(y)

What’s my rule?

3

?

0

5

1

6

2

7

3

slide2

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

slide4

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.

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

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

6

7

3

8

the function rule describes the relationship between each input and output

Input

(x)

output(y)

1

2

The function rule describes the relationship between each input and output.

0

5

6

Add 5

7

3

8

slide8

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

slide9

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

slide10

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

slide11

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

slide12

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

slide13

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
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!

slide16

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

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

we can make a graph of this rule by using the x and y as coordinates

Input

(x)

Input

(x)

output(y)

output(y)

1

1

2

2

3

3

4

4

8

8

12

12

16

16

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

y = 4x

4

slide20
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?

you can also write a rule from a graph using the coordinates

Input

(x)

output(y)

0

-1

1

1

2

3

3

5

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

Hint: make a table!

Y = 2x-1

slide25

Which equation fits the table?

  • y = x + 15
  • y = 10x + 5
  • y = 3x + 12
  • y = 15x
slide26

What’s the rule for this one?

Correct!

Divide by 2,

or y = 1/2 x

slide28

input(x)

output(y)

0

1

2

3

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

7

9

11

X = 15

13

slide29

input(x)

output(y)

?

0

1

2

3

See if you can guess the rule.

Correct! y = 4x + 1

1

5

9

13

slide30

input(x)

output(y)

1

0

2

2

3

4

4

?

Can you guess the rule?

I’ll give you a hint ~ make a table!

slide31

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

slide32

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.