Piecewise Functions 1

Friday, April 26th

Warm Up Graph the following equations by hand on

this graph!!

1) f(x) = x + 3

2) f(x) = 2x – 1

3) f(x)= x2

What is a piecewise function?

A function that uses different equations for different parts of its domain.

Basically, a bunch of functions put together in pieces!

We look at only one piece!Original Piecewise

02)( xxxf2)( xxf

Graphing with one piece

Step 1: Graph the original

Step 2: Put a line (“fence”) on the domain restriction

For example here, x = 2

Step 3: Greater or Less than? Erase the part you do not need! Since x is less than 2 (we want this piece!), Erase the part greater than 2, we don’t want that part!

2)( 2 xxxf

X Y

-2

-1

0

1

2

3

Step 4: Filled in circle or open at x=2? Fill in when you have an equal to sign!

Graphing with one piece

Step 1: Graph the original Step 2: Put a line on the

domain restriction

For example here, x = -3

Step 3: Greater or Less than? Erase the part you do not need! Since x is greater than -3 (we want this piece!), Erase the part less than -3, we don’t want that part!

31)( xxxf

X Y

-4

-3

-2

-1

0

1

Step 4: Filled in circle or open at x= -3? Fill in when you have an equal to sign!

Graphing with one piece

Step 1: Graph the original Step 2: Put a line on the

domain restrictions-two now!

For example, put up two “fences” at -1 and at 5!

Step 3: Now x is in between two numbers! Since x is between -1 & 5 (we want this piece!), Erase the parts outside of those two numbers, we don’t want that part!

513)( xxf

X Y

-2

-1

0

1

2

3

4

5

6Step 4: Filled in circle or open at x = -1 and x = 5? Fill in when you have an equal to sign! Who owns the fence?

You Try! DO the steps!

Step 1: Graph the original Step 2: Put a line on the

domain restriction

For example here, x = 4

Step 3: Greater or Less than? Erase the part you do not need! Since x is less than 4 (we want this piece!), Erase the part greater than 4, we don’t want that part!

423)( xxxf

X Y

0

1

2

3

4

5Step 4: Filled in circle or open at x = 4? Fill in when you have an equal to sign!

Once you get the hang of it you do not have to graph & erase—you can just graph the part you need!

You Try! DO the steps!

Step 1: Graph the original Step 2: Put up “fences” on

the domain restrictions

For example here, x = -2, 4

Step 3: Step 3: Now x is in between two numbers! Since x is between -2 & 4 (we want this piece!), Erase the parts outside of those two numbers, we don’t want that part!

425)( xxf

X Y

-3

-2

-1

0

1

2

3

4

Step 4: Filled in circle or open at x = -2 & 4? Fill in when you have an equal to sign! Who owns the fence?

Graphing with TWO pieces

This works the same way, you just go through the steps twice!

13

1)(

2

x

xxxf

X Y

-2

-1

0

1

2

3

X Y

-2

-1

0

1

2

3

2)( xxf 3)( xf

Graphing with TWO pieces

This works the same way, you just go through the steps twice!

32

231)(

x

xxxf

X Y

-4

-3

-2

-1

0

1

2

3

X Y

-4

-3

-2

-1

0

1

2

3

1)( xxf 2)( xf

What about evaluating?

How would you find the following?

f(-4) = f(-3) = f(1) =

32

231)(

x

xxxf

You Try! Do the steps twice!

This works the same way, you just go through the steps twice!

3

34)(

2 xx

xxxf

X Y

0

1

2

3

4

5

X Y

0

1

2

3

4

5

4)( xxf 2)( xxf

f(5) =

f(3)=

f(-1)=

You Try! Do the steps twice!

This works the same way, you just go through the steps twice!

24

21)(

2

x

xxxf

X Y

-1

0

1

2

3

4

X Y

-1

0

1

2

3

4

1)( 2 xxf 4)( xf

f(6) =

f(-3)=

f(2)=

Activity

Homework

Worksheet

PIECEWISE FUNCTIONS 2

April 26th, 2013

Warm UpComplete the piecewise graph…

143

1)(

2

xx

xxxf

X Y

0

1

2

3

4

5

X Y

0

1

2

3

4

5

Homework Solutions

X Y X Y

Remember…

What is a piecewise function?

How do we graph them?

Which equation do we plug certain x-values in to?

Review: Graphing with one piece

Step 1: Graph the original

FILL IN THE TABLE! Step 2: Put a line (“fence”)

on the domain restriction

For example here, x = 2

Step 3: Greater or Less than? Erase the part you do not need! Since x is less than 2 (we want this piece!), Erase the part greater than 2, we don’t want that part!

2)( 2 xxxf

X Y

-5

-4

-3

-2

-1

0

1

2Step 4: Filled in circle or open at x=2? Fill in when you have an equal to sign!

What values should we put in our table?

Now that we have learned how to graph, lets take some short cuts!

Look at the domain restrictions, ONLY make your table for the values you NEED.

Look to see if there is an “equal to” to see if you should include that number.

Then we won’t need to erase, this will help graph faster!

What if there is one table for two pieces?

Look at the domain restrictions, figure out which numbers from the table should be used for the first equation, and which numbers should be used for the second.

Find the “equal to” to see which equation you should use for that specific number.

Graphing with TWO pieces

Which equation should I use for the x values -2 to 0? 1 to 3?

13

1)(

2

xx

xxxf

Which equation should I use? 1st

or 2nd?

X Y

-2

-1

0

1

2

3

Graphing with TWO pieces

Which equation should I use for the x values -5 to -4? -3 to 0?

35

35)(

xx

xxf

Which equation should I use? 1st

or 2nd?

X Y

-5

-4

-3

-2

-1

0

Graphing with TWO pieces

Which equation should I use for the x values -3 to -1? 0 to 5?

512

11)(

2

x

xxxf

Which equation should I use? 1st or 2nd?

X Y

-3

-2

-1

0

1

2

3

4

5

You Try with TWO pieces

Which equation should I use for the x values -1 to 2? 3 to 4?

24

2)(

2

xx

xxxf

Which equation should I use? 1st

or 2nd?

X Y

-1

0

1

2

3

4

You Try with TWO pieces

Which equation should I use for the x values -4 to -2? -1 to 1?

23

23)(

xx

xxf

Which equation should I use? 1st

or 2nd?

X Y

-4

-3

-2

-1

0

1

Activity

Finish/Start Greeting Card Activity Work with a partner to complete the

activity. Write your answers/solutions neatly.

Each pair will present one question to the class.

Homework

Worksheet # 2