-23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is...
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Transcript of -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is...
![Page 1: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/1.jpg)
35−2
2−40
-23450-2
x y
?{(3,-2), (5,4), (-2,0)}
![Page 2: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/2.jpg)
A relation is set of ordered pairs, where one number is mapped to another number.
![Page 3: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/3.jpg)
We need to be able to show relations in a variety of forms. In each form, there are pairs
of numbers, where one number is considered the input and the other is the
output.
![Page 4: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/4.jpg)
I. Mappings
A Mapping looks like this:
35−2
2−40
This mapping contains three pairs: 3 is mapped onto -25 is mapped onto 4-2 is mapped onto 0
![Page 5: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/5.jpg)
II. Tables
A Table looks like this:
This relation contains the same pairs as the mapping we just saw.
(The names at the top of the table do NOT have to be x and y!)
-23450-2
x y
![Page 6: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/6.jpg)
III. Coordinate Graphs
A Coordinate Graph looks like this:
To plot pairs on a coordinate plane, the first number tells you how far to
the right or left of the origin to go, the second number is up or down.
(3,-2)
(5, 4)(-2,0)
![Page 7: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/7.jpg)
IV. Sets of Ordered Pairs
A Set of Ordered Pairs looks like this:
We always put sets in braces { } and separate elements by commas. The
order is easy to determine here!
{(3,-2), (5,4), (-2,0)}
![Page 8: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/8.jpg)
V. Input-Output Machines
An Input-Output Machine looks like this:
The arrows show which number is the first number (the input) and which is
the second (the output).
?
3
-2
![Page 9: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/9.jpg)
Re-Writing RelationsThis relation is in mapping form.
Write a table for this relation.
-2
3
4
7
-1
0
4
4-20304
a b
7 -1
NOTE: Some relations use the same values more than once.
![Page 10: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/10.jpg)
Re-Writing RelationsThis relation is in set form.
Draw a mapping for this relation.
{(1, 5), (0, 4), (4, 8), (-7, -3)}
-7
0
1
4
-3
4
5
8
![Page 11: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/11.jpg)
The last relation had a pattern to it. Did you notice?
{(1, 5), (0, 4), (4, 8), (-7, -3)}
Some relations are created by some set of operations, a formula that maps one
number to another number.
![Page 12: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/12.jpg)
Formula Relations
{(1, 5), (0, 4), (4, 8), (-7, -3)}
In each pair, the second number is 4 more than the first number, the formula
for this relation could be written:
y = x + 4.Or use different letters:
w = r + 4.
![Page 13: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/13.jpg)
A Formula Machine
x + 4
1 0 4
5 4 8
Input:
Output:
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?
2−
−4
7
14
21
1
What formula creates this relation?
![Page 15: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/15.jpg)
2⋅x
2−
−4
7
14
21
1
What formula creates this relation?
![Page 16: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/16.jpg)
5-1
100
1218
1173 ?
This relation follows a formula, find the formula & decide what 3 maps onto.
![Page 17: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/17.jpg)
20
5-1
100
1218
1173 ?
The formula is “add 17 to each input”, x + 17. 3 maps onto 20.
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5-1
100
1218
117? 0
What number maps onto 0?
17-
![Page 19: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/19.jpg)
?
Find the output values if the input values are {1, 3, 5,
7}.
25+x
1
3
Input Output
1 3
![Page 20: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/20.jpg)
?
Find the output values if the input values are {1, 3, 5,
7}.
25+x
3
4
Input Output
1 33 4
![Page 21: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/21.jpg)
?
Find the output values if the input values are {1, 3, 5,
7}.
25+x
5
5
Input Output
1 33 45 5
![Page 22: -23 45 0 xy ? {(3,-2), (5,4), (-2,0)}. A relation is set of ordered pairs, where one number is mapped to another number.](https://reader031.fdocuments.in/reader031/viewer/2022020718/56649f295503460f94c42160/html5/thumbnails/22.jpg)
?
Find the output values if the input values are {1, 3, 5,
7}.
25+x
7
6
Input Output
1 33 45 57 6