3.1 representing relations objectives the student will be able to: 1.represent relationship among...
TRANSCRIPT
![Page 1: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/1.jpg)
3.1 Representing RelationsObjectives
The student will be able to:
1.represent relationship among quantities using tables, graphs, and diagrams
2.identify mathematical domains and ranges
3.identify the inverse of a relation.
Indicators: PFA #1, PFA#7
Designed by Skip Tyler, Varina High SchoolModified by Anny Lin, Crestwood Middle School
![Page 2: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/2.jpg)
How about some more definitions? The domain is the
set of 1st coordinates of the ordered pairs.
The range is the
set of 2nd coordinates of the ordered pairs.
A relation is a
set of ordered pairs.
![Page 3: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/3.jpg)
Given the relation {(3,2), (1,6), (-2,0)},
find the domain and range.
Domain = {3, 1, -2}
Range = {2, 6, 0}
![Page 4: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/4.jpg)
What would this be?
{(2,4), (3,-1), (0,-4)}
A lame relationship!! Ha! Ha!
![Page 5: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/5.jpg)
The relation {(2,1), (-1,3), (0,4)} can be shown by
1) a table.
2) a mapping.
3) a graph.
x y2-10
134
2-10
134
![Page 6: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/6.jpg)
Given the following table, show the relation, domain, range, and mapping.
x -1 0 4 7y 3 6 -1 3
Relation = {(-1,3), (0,6), (4,-1), (7,3)}
Domain = {-1, 0, 4, 7}
Range = {3, 6, -1, 3}
![Page 7: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/7.jpg)
Mappingx -1 0 4 7y 3 6 -1 3
You do not need to write 3 twice in the range!
-1047
36-1
![Page 8: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/8.jpg)
What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)}
1. {2, 3, 4, 4}
2. {1, 2, 3, 1}
3. {2, 3, 4}
4. {1, 2, 3}
5. {1, 2, 3, 4}
Answer Now
![Page 9: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/9.jpg)
What is the range of the relation{(2,1), (4,2), (3,3), (4,1)}
1. {2, 3, 4, 4}
2. {1, 2, 3, 1}
3. {2, 3, 4}
4. {1, 2, 3}
5. {1, 2, 3, 4}
Answer Now
![Page 10: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/10.jpg)
Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x).
Write the relation and the inverse.
Relation = {(-1,-6), (3,-4), (3,2), (4,2)}
Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}
-134
-6-42
![Page 11: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/11.jpg)
Write the inverse of the mapping.
-3
43-12
1. {(4,-3),(2,-3),(3,-3),(-1,-3)}
2. {(-3,4),(-3,3),(-3,-1),(-3,2)}
3. {-3}
4. {-1, 2, 3, 4} Answer Now
![Page 12: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/12.jpg)
http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/extra_examples/chapter4/lesson4_3.pdf
![Page 13: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/13.jpg)
![Page 14: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/14.jpg)
![Page 15: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/15.jpg)
c. What conclusions might you make from the graph of the data?
The number of departures of U.S. commercial airlines has increased each year. This may be due to the safer conditions or less expensive airline tickets.
![Page 16: 3.1 Representing Relations Objectives The student will be able to: 1.represent relationship among quantities using tables, graphs, and diagrams 2.identify](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f275503460f94c3f0f7/html5/thumbnails/16.jpg)
Homework: Page 146 13-21 all and 23, 25, 27