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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)= x 2. What is a piecewise function?. A function that uses different equations for different parts of its domain. - PowerPoint PPT Presentation
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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