Bell Work

In Out

4 97 12

10 15

Find the pattern and fill in the numbers then write the function rule.

Function rule: y= x + 5

13 1816 2119 24

Function Rules

What is a function?

It could be thought of as a Function Machine where certain inputs go in and certain outputs come out.

Suppose we put some numbers in our Function Machine and certain numbers come out.

3 ,

5 ,

4 ,

5 ,

6

6 ,

7 ,

8

Do you see a pattern between the inputs and outputs?Pattern: Add 2 to the input to get the output.

Predict what will happen when we put 10 in our Function Machine.

3 ,

5 ,

4 ,

5 ,

6,…

6 ,

7 ,

8,…

12

10

Pattern: Add 2 to the input to get the output.

REMINDER:

Predict what number must be put in our Function Machine to get an output of 15.

3 ,

5 ,

4 ,

5 ,

6,…

6 ,

7 ,

8,…,

12,

10,

15

13

Pattern: Add 2 to the input to get the output.

REMINDER:

What is the function of this machine?

3 ,

5 ,

4 ,

5 ,

6,…,

6 ,

7 ,

8,…,

12,

10,

15

13

+ 2

We can write this as a function rule:y = x + 2, x is the input and y is the output.

Writing a Function Rule

Write a function rule for the input-output table.

SOLUTION

What is the pattern?

A function rule for the input-output table is y = x + 2.5.

ANSWER

Add 2.5 to each input x to get the output y.

What is the function rule?

y = x + 2.5

+2.5+2.5+2.5+2.5+2.5+2.5+2.5

Write a function rule for the input-output table.SOLUTION

5xy

What is the pattern?Add 5 to each input x to get the output y.

What is the function rule?

A function rule for the input-output table is y = x + 5.

ANSWER

+5

+5

+5

+5

+5

Example:

Making Cuts

In the cheese-slicing diagram below, the input c is the number of cuts made across the center of the cheese, and the output p is the resulting total number of pieces of cheese. Write a rule for the function. Then use the rule to find the number of pieces made with 9 cuts.

STEP 1

Make an input-output table.

STEP 2Write a function rule. Notice that each output value is twice the input value. So, a rule for the function is p = 2c.

x 2

x 2

x 2

x 2

STEP 3

p = 2(9)

p = 18

So there are 18 pieces made with 9 cuts.

Evaluate the function when c = 9 to find the number of pieces made with 9 cuts.

Write a function rule for the input-output table. Then use the rule to find the output y when x = 12.

You Try:

SOLUTION

What is the pattern?

Subtract 3 to each input x to get the output y.

What is the function rule?

y = x - 3

y = x – 3 Write original equation.

y = 12 – 3 Substitute x = 12

y = 9 Simplify.

-3 -3 -3 -3

Write a function rule for the input-output table. Then use the rule to find the output y when x = 12.

YOU TRY!

SOLUTION

What is the pattern?

Divide each input x by -2 to get the output y.

What is the function rule?

Write original equation.

Substitute x = 12

Simplify.

2x

y

2

12

y

6y

2x

y

-2

STEP 1Find the value of a usinginputin change

outputin changea

STEP 2Plug a into the equation y = ax + b.

To find b, substitute an input-output pair for x and y.

STEP 3

STEP 4 Plug value of b into the equation y = ax + b to obtain the function rule.

Sometimes we can’t see the pattern right away.

4 Steps for writing a function rule:

Write a function rule that relates x and y.SOLUTION

Find the value of a.

Plug value of a into y = ax + bFind b by substituting an input-output pair for x and y.

Plug value of b into y = ax + b

bxy 1

5xy

Function rule that relates x and y.

2

2

inputin change

outputin changea 1

Let (x, y)= (0, 5)

5 = 1(0)+ b, so b = 5

Example:

SOLUTION

If you double the position number and subtract 3, you get the value of the term. So, the correct answer is B.

+2

+2

+2

+2

+2

+1

+1

+1

+1

+1

1

2

inputin change

outputin changea

bxy 2

2

32 xy

Find the value of a.

Plug value of a into y = ax + b

Find b by substituting an input-output pair for x and y.

Plug value of b into y = ax + b

Let (x, y)= (2, 1)

1 = 2(2)+ b, so b = -3

ANSWER

Write a function rule that relates x and y.+1 +1 +1 +1

+3 +3 +3 +3

Find the value of a.

Plug value of a into y = ax + b

Find b by substituting an input-output pair for x and y.

Plug value of b into y = ax + b

1

3

inputin change

outputin changea

bxy 3

13 xy

3

Function rule that relates x and y.

Let (x, y)= (1, 2)

2 = 1(1)+ b, so b = -1

YOU TRY!

Write a function rule that relates x and y in the table at the right.

SOLUTION

You Try!

Find the value of a.

Plug value of a into y = ax + b

Find b by substituting an input-output pair for x and y.

Plug value of b into y = ax + b

1

1

inputin change

outputin changea

bxy 1

8xy

1

Function rule that relates x and y.

Let (x, y)= (1, -7)

-7 = 1(1)+ b, so b = -8

+1 +1 +1

+1 +1 +1

Practice: