**Lesson 4.4:**

Writing a Function rule

Writing a Function rule

Introduction:

A function rules is an equation used to describe a function; or what you plug into x to get y.

The function rule is the equation that describes the relationship between the input and output.

x (input)

y (output)

Function rule (machine):

An the equation that turns

the x (input) into y (output)

Demonstration:

X

0

2

4

6

F(x)

3

5

7

9

Example 1

When writing a function rule, just ask yourself how can I get:

0 to 3

2 to 5

4 to 7

6 to 9

The Function Rule is:

f(x)= x + 3

Example 2

X

0

1

3

5

Y

0

3

9

15

Check your work by pluging in numbers into f(x)= n+3

3= 0+3; yes

5= 2+3; yes

7= 4+3; yes

9= 6+3; yes

Again, ask yourself how to get:

0 to 0

1 to 3

3 to 9

5 to 15

The answer to this example is

f(x)= 3n

Then, check your work by plugging your numbers into

f(x)= 3n

0= 3(0)

3= 3(1)

9= 3(3)

15= 3(5)

Example 3

Write a function rule for this situation

You get paid $10 for each good grade you get on a test.

Paying attention to key words, you can conclude that:

The output is how much you get paid

The input is how much good grade test you get

So the function is: f(g)= $10g

Question 3.1: how much are you paid if

you get 3 good grades on a test

Plug 3 (the number of test), which is the g (or x)

variable into the function rule to get:

f(g)= $10(3) and then $30

**Pre-Reqs**

Before starting the demonstrations, you will have to now that we will be writing function rules off of table of values and situations.

The format for a function rule (for now)

is y= (function rule) x

Also that f(x) = the function of x

f(c)= the function of c

f(z)= the function of z

Problems

Problem 1:

Solve:

X

-3

-1

1

3

F(X)

-1

1

3

5

Problem 2:

Solve

X

0

3

6

9

F(X)

0

6

12

18

**Guided Problems**

**x**

-5

0

1

4

-5

0

1

4

**f(x)**

13

-2

-5

-12

13

-2

-5

-12

**Problem 1**

**Problem 2**

**x**

-3

0

1

5

-3

0

1

5

**f(x)**

-10

-1

2

14

-10

-1

2

14

**Problem 3**

**Write an equation to represent this situation:**

The weight of a bag of candy depends on how much pieces of candy you have when each piece of candy weighs .15 lbs.

How much would a bag of candy weigh if there was 5 pieces of candy?

The weight of a bag of candy depends on how much pieces of candy you have when each piece of candy weighs .15 lbs.

How much would a bag of candy weigh if there was 5 pieces of candy?

**Problem 4**

**Write an equation to represent this situation:**

The amount of pizza that a bro would bring to a party depends on 3 times as much bros at the party divided by eight.

The amount of pizza that a bro would bring to a party depends on 3 times as much bros at the party divided by eight.

**Problem 3**

Solve:

Solve:

**X**

-3

0

1

4

-3

0

1

4

**F(X)**

.5

2

2.5

4

.5

2

2.5

4

**Problem 4**

**Write an eauation to represent this situation:**

The amount you get paid for a job that pays $15 for every hour.

How much would you get paid after you work for 8 hours?

The amount you get paid for a job that pays $15 for every hour.

How much would you get paid after you work for 8 hours?

**Problem 5**

Example 4

Write a situation that models the equation:

y= 3+x

Pay attention to the positions of the variable, y is the dependent variable and x is the independent vairable.

So...

That means that 3+x is the function

So let your creativity flow and your mind wander to solve this problem.

Write an equation to represent this situation:

A man gets rewarded 5 dollars for every time he walks to work.

How many dollars does he receive after walking to work 17 times.

**Agenda**

**SPEAK OUT**

Pre-Req

Demonstrations

Guided problems

Practice Problems

Pre-Req

Demonstrations

Guided problems

Practice Problems

**Problem 6**

**Write a situation that represents this equation:**

f(x)= 100x

f(x)= 100x

When solving a function rule, just remember that the function rule is the equation in the format y=_____ x

Example: if the funxtion rule was y=7+x, and x was 3, y would equal 10

APRIL , 2016

SPEAK OUT: 1. Given the functions: f(x)= 5x-2 and g(x)= 2x+5

Evaluate the following:

a. f(2)-g(3)

CQ: How can we understand the symbols and notation of function?

Today's topic: Writing a function rule

April 15, 2016

CQ: How do we master our function unit?

Today's Goal:

Group A and B- Function Quiz

Group C- Function transformation

SPEAK OUT: Write a relation that is a function, one that is not a function

April 19, 2016

CQ: How can we use our knowledge of functions to explore transformation?

Today's Goal:

Group A and B- Delta Math Mastery sheet

Group C- Transformation

May 3, 2015

SPEAK OUT: Evaluate the following function:

f(x)= x-3 g(x)= 3x+2

a. f(10) b. g(6) c. f(2) * g(6)

CQ: How can we use our knowledge of functions to explore transformation?