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Function Notes
1
December 15, 2014
Functions and Relations
Lesson objectives Teachers' notes
Objectives:1) Summarize the definition of a function both visually and in your own words.
2) Apply definition to sets of relations and graphs to determine if they are functions.
Function Notes
2
December 15, 2014
Teachers' notesLesson objectives
Subject:
Topic:
Grade(s):
Prior knowledge:
Crosscurricular link(s):
Algebra II
Functions and Relations
910
Type text here
Type text here
Lesson notes:
Focus Question:How can we determine if a given graph or set of relations is a function?
Function Notes
3
December 15, 2014
What is a function?It is a special kind of relation.
Real Life Examples:Age Example:Height exampleYour Example???
Function Notes
4
December 15, 2014
Consider these numbers...Consider these numbers...2 and 105 and 257 and ??7 and 35
Have you figured out the relation between these numbers?relation
2 and -105 and -257 and ??7 and -35
Function Notes
5
December 15, 2014
relationA relation in mathis some numbers that are connectedto other numbers by a pattern.
ordered pairThe connected numbers
make an ordered pair.
(2,10)
(2,-10)
(5,25)(5,-25)
(7,35)(7,-35)
Function Notes
6
December 15, 2014
x y2 -102 105 -255 257 -357 35
(2,10)(2,-10)
(5,25)(5,-25)
(7,35)(7,-35)
There are lots of ways to show a relation.
ListList TableTable MapMap GraphGraph EquationEquationy=±5x
Function Notes
7
December 15, 2014
1
0
-1
-2
2
-3
-2-1
0
1
In this relation, what is the output when the input is 1 ?
In this relation, what is the value of x when y=-2 ?
Function Notes
8
December 15, 2014
In this relation, what is the output when the input is 3 ?
In this relation, what is the value of x when y=1 ?
1
2
3
4
1
2
0
-1
Function Notes
9
December 15, 2014
In this relation, what is the value of x when y=0 ?
In this relation, what is the output when the input is 0 ?
{( , ), ( , ), ( , ), ( , ), ( , )}-1 0 5-3-5 243-1 0 4
Function Notes
10
December 15, 2014
In this relation, what is the value of x when y=-2 ?
0
1
2
3
4
5
-1
-2
-3
-4
-5
1 2 3 4 5-1-2-3-4-5
In this relation, what is the output when the input is 1 ?
Function Notes
11
December 15, 2014
What makes the values in a table a function?
• With a table, the condition means that if there are two rows of a table with the same “input” then they must also have the same output.
Function Notes
12
December 15, 2014
1 2
1000 200050 100
5 102 4
7 14
in out
function machine
Function Notes
13
December 15, 2014
Domain
The domain contains the numbers or values called the inputs.
x y
1
42
2
63
84
50
100
Function Notes
14
December 15, 2014
Range
The range contains the numbers or values called the outputs.
x y
1
42
2
63
84
50
100
Function Notes
15
December 15, 2014
Function:
A special relation such that for all xvalues(input) there exists one and only one y value.
Function Notes
16
December 15, 2014
The “Pairing” of names and heights is a relation.
Pairs of names and heights are “ordered” in functions.
(Person, Height)
OnetoOne
Function Notes
17
December 15, 2014
(Height, Person)
Not a Function
Function Notes
18
December 15, 2014
Mapping:
Function Notes
19
December 15, 2014
NOTES TIME!
•Use notes section of binder•Examples have no errors•110% attention necessary•Teacher is the only one talking
Function Notes
20
December 15, 2014
Function:Well behaved relation.
Definition: A special relation such that for all values of x there exists one and only one yvalue.
OnetoOne
Function Notes
21
December 15, 2014
Function Notes
22
December 15, 2014
Set of relations:
1. {(2, 3), (4, 5), (5, 6)}
2. {(2, 3), (4, 3), (5, 6)}
3. {(2, 3), (2, 5), (5, 6)}
Yes
No
Yes
Function Notes
23
December 15, 2014
Graphs:
Vertical Line Test:
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
4
5
6
90°
Function Notes
24
December 15, 2014
Function Notes
25
December 15, 2014
Function Notation:
Example:Linear Function:y = 2x 1
Function Notes
26
December 15, 2014
4
8
2
4
5
What's my rule?Click on the green arrow and drag over to the IN slot and then drag it down into the Function Machine. The answer will appear from the OUT slot.Try all three inputs and see if you can determine the rule. Tip my hat to see if you are correct.
NextNext
IN
OUT
x 2
Function Notes
27
December 15, 2014
Input Output
2
4
5
4
8
10
Now that you know the rule see if you can enter some other Inputs and then determine the Outputs.
Take the Input --- Apply the Rule --- Get the Output
NextNext
Function Notes
28
December 15, 2014
6
13
10
21
7
What's my rule?Click on the green arrow and drag over to the IN slot and then drag it down into the Function Machine. The answer will appear from the OUT slot.Try all three inputs and see if you can determine the rule. Tip my hat to see if you are correct.
IN
OUT
NextNext
x 2
Function Notes
29
December 15, 2014
Input Output
6
7
10
13
15
21
Now that you know the rule see if you can enter some other Inputs and then determine the Outputs.
Take the Input --- Apply the Rule --- Get the Output
NextNext
Function Notes
30
December 15, 2014
Pay close attention to
the summary on the next slides!
Function Notes
31
December 15, 2014
Relation: simply a set of ordered pairs.
List the domain and range for each set above.
Function Notes
32
December 15, 2014
A function is a rule that relates two quantities so that each input value (domain) corresponds to exactly one output value (range). "one-to-one"
Functions can often be looked at as input-output machines.
Let's practice with some function "machines".
Machine #2Machine #1
List the ordered pairs:
List the ordered pairs:
Is the relation a function?
http://www.amblesideprimary.com/ambleweb/mentalmaths/functionmachines.htmlhttp://www.littlefishsw.co.uk/card/functionmachine.html
Function Notes
33
December 15, 2014
Vertical Line TestThis test can be used to see if a graph represents a function.To be a function a vertical line can only touch the graph at one point.
Practice
http://www.shodor.org/interactivate/activities/VerticalLineTest/
Function Notes
34
December 15, 2014
Functions can also be illustrated with input-output tables or x-y tables.
Use the rule y = 2x to complete the table
Does the graph pass the vertical line test?
Function Notes
35
December 15, 2014
Use the rule y = 3x - 1to complete the table
Does the graph pass the vertical line test?
Function Notes
36
December 15, 2014
Use the rule y = x2 + 3to complete the table
Graph the ordered pairs
Does the graph pass the vertical line test?
Function Notes
37
December 15, 2014
Practice # 1
Practice # 2
Practice # 3
Function Notes
38
December 15, 2014
Practice #1
Function Notes
39
December 15, 2014
Quiz
Decide if each of the following represents a function.
1. {(1, 3), (2, 5), (3, 6), (4, 12)}2. {(0, 4), (0, 5), (1, 5)}3. {(5, 1), (3, 1), (-2, 1), (4, 1)}4. y = 2x + 1, if x = {1, 2, 3}5. y = x - 5, if x = {2, 4, 6}
Function Notes
40
December 15, 2014
What did I learn last class?Determine if the following is a relation or a funtion and give the domain and range
x y1 102 123 144 165 18
x y2 124 82 44 00 4
x y8 84 40 04 48 8
x y2 26 618 1854 54
162 162
Function Notes
41
December 15, 2014
Graph the relation and determine the domain and range.
{(2, 1), (3, 5), (5, 12)}
6 5 4 3 2 1 0 1 2 3 4 5 6
6
5
4
3
2
1
1
2
3
4
5
6
x
yDomain:
Range:
Function Notes
42
December 15, 2014
Guided Practice:
Ex#1f(x) = 3x 2 h(x) = 2x + 1 g(x) = 5x
f(1) =f(0) = h(2) =g(5) = g(1/5) =
Function Notes
43
December 15, 2014
Guided Practice:
Ex#2Create a table for each of the functions: f(x) = 3x 2 h(x) = 2x + 1
x 3x 2 f(x) x 2x + 1 f(x)
Function Notes
44
December 15, 2014
From the Sleep Inn, Sam jumped out of the window and walked 2 miles north and 4 miles east to the hideout spot. If the origin represents the Sleep Inn, graph the point that represents the hideout spot.
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
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Jul 28-2:04 PM Every equation is a relation.1Only some relations are functions.2In a function, every input has one and only one output.3For Graphs: use the vertical line test .45falsetrue Is It a Function?
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SMART Notebook
AFunction Tables
Complete the function table for each equation.
Name: Date:
Copyright ©2010 WorksheetWorks.com
x y
-2
-1
5
9
y = 3x G 3( 1 )
x y
-6
1
2
5
y = x Q 2( 2 )
x y
-9
-7
3
4
y = x G 6( 3 )
x y
-3
-1
1
5
y = x Q 3( 4 )
x y
-7
-5
0
4
y = x G 2( 5 )
x y
-9
-6
0
2
y = x G 1( 6 )
x y
-9
-8
-4
1
y = 3x G 4( 7 )
x y
0
2
4
5
y = Gx Q 5( 8 )
x y
-6
-4
-1
3
y = x G 4( 9 )
x y
-2
-1
0
1
y = x Q 1(10)
x y
-9
-8
-4
8
y = x Q 4(11)
x y
-7
-5
0
6
y = 3x G 2(12)
AFunction Tables
Complete the function table for each equation.
A N S W E R K E Y
Copyright ©2010 WorksheetWorks.com
x y
-2
-1
5
9
y = 3x G 3( 1 )
x y
-6
1
2
5
y = x Q 2( 2 )
x y
-9
-7
3
4
y = x G 6( 3 )
x y
-3
-1
1
5
y = x Q 3( 4 )
x y
-7
-5
0
4
y = x G 2( 5 )
x y
-9
-6
0
2
y = x G 1( 6 )
x y
-9
-8
-4
1
y = 3x G 4( 7 )
x y
0
2
4
5
y = Gx Q 5( 8 )
x y
-6
-4
-1
3
y = x G 4( 9 )
x y
-2
-1
0
1
y = x Q 1(10)
x y
-9
-8
-4
8
y = x Q 4(11)
x y
-7
-5
0
6
y = 3x G 2(12)
-9
-6
12
24
-4
3
4
7
-15
-13
-3
-2
0
2
4
8
-9
-7
-2
2
-10
-7
-1
1
-31
-28
-16
-1
5
3
1
0
-10
-8
-5
-1
-1
0
1
2
-5
-4
0
12
-23
-17
-2
16
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http://www.WorksheetWorks.com/math/geometry/graphing/function-table.html
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SMART Notebook
AFunction Tables
Complete the function table for each equation.
Name: Date:
Copyright ©2010 WorksheetWorks.com
x y
-7
-3
-2
7
y = x Q 5( 1 )
x y
-7
-6
-3
5
y = x G 4( 2 )
x y
-9
3
8
9
y = x G 1( 3 )
x y
-8
-3
2
7
y =1-4x Q 4( 4 )
x y
-5
-1
2
9
y = x G 6( 5 )
x y
-5
-2
0
6
y = x G 5( 6 )
x y
-9
-2
5
8
y = x Q 2( 7 )
x y
-8
-3
4
6
y = G4x( 8 )
x y
-9
-7
-3
-2
y = G3x( 9 )
x y
-3
-2
6
7
y =14x Q 1(10)
x y
-8
-2
4
5
y = 3x(11)
x y
-9
-8
-2
4
y =14x G 5(12)
AFunction Tables
Complete the function table for each equation.
A N S W E R K E Y
Copyright ©2010 WorksheetWorks.com
x y
-7
-3
-2
7
y = x Q 5( 1 )
x y
-7
-6
-3
5
y = x G 4( 2 )
x y
-9
3
8
9
y = x G 1( 3 )
x y
-8
-3
2
7
y =1-4x Q 4( 4 )
x y
-5
-1
2
9
y = x G 6( 5 )
x y
-5
-2
0
6
y = x G 5( 6 )
x y
-9
-2
5
8
y = x Q 2( 7 )
x y
-8
-3
4
6
y = G4x( 8 )
x y
-9
-7
-3
-2
y = G3x( 9 )
x y
-3
-2
6
7
y =14x Q 1(10)
x y
-8
-2
4
5
y = 3x(11)
x y
-9
-8
-2
4
y =14x G 5(12)
-2
2
3
12
-11
-10
-7
1
-10
2
7
8
6
4 343 122 14
-11
-7
-4
3
-10
-7
-5
1
-7
0
7
10
32
12
-16
-24
27
21
9
6
1412
2 122 34
-24
-6
12
15
-7 14-7
-5 12-4
a a
a aThis is a genuine, customized
worksheet from
ACreated by 168.8.172.2 on Nov 30, 2010 2:27:56 PM GMT
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SMART Notebook
AFunction Tables
Complete the function table for each equation.
Name: Date:
Copyright ©2010 WorksheetWorks.com
x y
-8
6
7
8
y = 3x Q 1( 1 )
x y
-6
-4
0
8
y = Gx Q 5( 2 )
x y
-5
1
8
9
y = G2x Q 4( 3 )
x y
-9
-7
4
6
y = G2x Q 2( 4 )
x y
4
5
8
9
y = x Q 1( 5 )
x y
-512
-1
112
5
y = 2x G 3( 6 )
x y
-9
-6
-4
-1
y = G4x Q 3( 7 )
x y
-9
-4
-1
7
y = x G 4( 8 )
x y
-9
-8
3
8
y = x G 6( 9 )
x y
-9
-8
-412
-212
y = 4x G 6(10)
x y
-9
-4
-3
1
y = G3x G 6(11)
x y
-4
1
3
7
y = x G 3(12)
AFunction Tables
Complete the function table for each equation.
A N S W E R K E Y
Copyright ©2010 WorksheetWorks.com
x y
-8
6
7
8
y = 3x Q 1( 1 )
x y
-6
-4
0
8
y = Gx Q 5( 2 )
x y
-5
1
8
9
y = G2x Q 4( 3 )
x y
-9
-7
4
6
y = G2x Q 2( 4 )
x y
4
5
8
9
y = x Q 1( 5 )
x y
-512
-1
112
5
y = 2x G 3( 6 )
x y
-9
-6
-4
-1
y = G4x Q 3( 7 )
x y
-9
-4
-1
7
y = x G 4( 8 )
x y
-9
-8
3
8
y = x G 6( 9 )
x y
-9
-8
-412
-212
y = 4x G 6(10)
x y
-9
-4
-3
1
y = G3x G 6(11)
x y
-4
1
3
7
y = x G 3(12)
-23
19
22
25
11
9
5
-3
14
2
-12
-14
20
16
-6
-10
5
6
9
10
-14
-5
0
7
39
27
19
7
-13
-8
-5
3
-15
-14
-3
2
-42
-38
-24
-16
21
6
3
-9
-7
-2
0
4
a a
a aThis is a genuine, customized
worksheet from
ACreated by 168.8.172.2 on Nov 30, 2010 2:30:10 PM GMT
http://www.WorksheetWorks.com/math/geometry/graphing/function-table.html
Reproduction and Usage Rights
This worksheet may be used one time for educational purposes in a home or classroomfor up to fifty students. Permission to create printed copies of any part of this document islimited to the person who downloaded it. Reproduction for an entire school or schooldistrict is prohibited. No part of this document may be reproduced (except for theeducational use just mentioned), stored in a retrieval system, or transmitted in any form orby any means (other than to the printer, obviously) without prior written consent ofWorksheetWorks.com.
Adobe Acrobat Usage Tips
Conserve paper by printing only the pages you need. Learn aboutAcrobat's printing options.
•
Use Acrobat's shortcut keys to view and navigate PDFdocuments like a pro.
•
Configure how Acrobat opens documents downloaded from theInternet.
•
Visit http://www.WorksheetWorks.com/faq.html formore information about creating and printingworksheets online using Adobe Acrobat.
http://www.WorksheetWorks.com/math/geometry/graphing/function-table.html
http://www.WorksheetWorks.com/faq.html
SMART Notebook
Page 1: Nov 4-10:26 AMPage 2: Nov 4-10:26 AMPage 3: Aug 2-8:13 PMPage 4: Oct 1-9:50 PMPage 5: Oct 1-9:50 PMPage 6: Oct 1-9:50 PMPage 7: Oct 1-9:50 PMPage 8: Oct 1-9:50 PMPage 9: Oct 1-9:50 PMPage 10: Oct 1-9:50 PMPage 11: Teacher notes 2Page 12: Function Ex. 1Page 13: Domain contentPage 14: Range contentPage 15: Mar 19-7:45 AMPage 16: Aug 2-8:28 PMPage 17: Aug 2-8:29 PMPage 18: Aug 3-6:48 AMPage 19: Aug 2-8:44 PMPage 20: Mar 19-7:45 AMPage 21: Aug 2-8:46 PMPage 22: Aug 3-6:54 AMPage 23: Aug 3-7:09 AMPage 24: Nov 13-7:35 AMPage 25: Aug 3-7:29 AMPage 26: Function IVPage 27: Function IV ChartPage 28: Function VPage 29: Function V ChartPage 30: Nov 30-4:44 PMPage 31: Nov 30-8:47 AMPage 32: Nov 30-8:49 AMPage 33: Nov 30-9:14 AMPage 34: Nov 30-9:19 AMPage 35: Nov 30-9:22 AMPage 36: Nov 30-9:23 AMPage 37: Nov 30-9:24 AMPage 38: Dec 1-2:33 PMPage 39: Dec 1-11:24 AMPage 40: Nov 12-7:25 AMPage 41: Nov 30-4:45 PMPage 42: Aug 3-8:37 AMPage 43: Aug 3-2:47 PMPage 44: Dec 2-7:46 AMAttachments Page 1
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