Transcript Notes 1 - Henrico

3
5
2
?
2
4
0
{(3,-2), (5,4), (-2,0)}
x
3
5
-2
y
-2
4
0
A relation is set of ordered
pairs, where one number is
mapped to another number.
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.
I. Mappings
A Mapping looks like this:
3
5
2
2
4
0
This mapping contains three pairs:
3 is mapped onto -2
5 is mapped onto 4
-2 is mapped onto 0
II. Tables
A Table looks like this:
x
3
5
-2
y
-2
4
0
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!)
III. Coordinate Graphs
A Coordinate Graph looks like this:
(5, 4)
(-2,0)
(3,-2)
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.
IV. Sets of Ordered Pairs
A Set of Ordered Pairs looks like this:
{(3,-2), (5,4), (-2,0)}
We always put sets in braces { } and
separate elements by commas. The
order is easy to determine here!
V. Input-Output Machines
An Input-Output Machine looks like this:
3
?
-2
The arrows show which number is the
first number (the input) and which is
the second (the output).
Re-Writing Relations
This relation is in mapping form.
Write a table for this relation.
-2
3
-1
0
4
7
4
a
-2
3
4
7
b
4
0
0
-1
NOTE: Some relations use the same
values more than once.
Re-Writing Relations
This relation is in set form.
Draw a mapping for this relation.
{(1, 5), (0, 4), (4, 8), (-7, -3)}
-7
0
-3
4
1
4
5
8
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.
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.
A Formula Machine
Input:
1
0
4
x+4
Output:
5
4
8
What formula creates this
relation?
2
7
1
2
?
4
14
1
What formula creates this
relation?
1
2 7
2
2x
4
14
1
This relation follows a formula, find the
formula & decide what 3 maps onto.
-5
1
100
3
12
18
117
?
The formula is “add 17 to each
input”, x + 17. 3 maps onto 20.
-5
1
100
3
12
18
117
?
20
What number maps onto 0?
-5
1
100
-17
?
12
18
117
0
Find the output values
if the input values are {1, 3, 5, 7}.
1
x5
2
?3
Input
1
Output
3
Find the output values
if the input values are {1, 3, 5, 7}.
3
Input
Output
x5
2
?4
1
3
3
4
Find the output values
if the input values are {1, 3, 5, 7}.
5
Input
Output
x5
2
?5
1
3
3
5
4
5
Find the output values
if the input values are {1, 3, 5, 7}.
7
Input
Output
x5
2
6?
1
3
3
5
7
4
5
6