Introduction to Relations and Functions

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Introduction to Relations and Functions
A relation is a set of order pairs
A Function is a rule between an input and an
output
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One to One-This is a function For each input,
there is excalty one output.
?
1 2 3 4 5
5 6 7 8 9
?
?
?
?
Output
Input
The Rule is ADD 4
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Not A Function!! But it is a relation.
Paris London Italy New York Hawaii
Ahmed Peter Ali Mike Joe
?
?
?
?
Has Visited
There are MANY arrows from each person and each
place is related to MANY People. It is a MANY to
MANY relation. This is not a function because an
input can only go to ONE Output!
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Person Has A Mass of
Kg
?
Bill Peter Sally Alli George Amanda
62 64 66
?
?
?
?
?
In this case each person has only one mass, yet
several people have the same Mass. This is a
MANY to ONE relationship This is a function!
More than one input can have the same output.
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Is the length of
cm
object
Pen Pencil Ruler Needle Stick
?
?
14 30
?
?
?
Here one amount is the length of many
objects. This is a ONE to MANY relationship
Is this a function?
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Lets create our own relations. Going around the
room. Give me some numbers
Are they functions?
Now on the wipe-off board. Give me a relation
that is a function and give me one that is not a
function.
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Function - Domain and Range!
y?2x1
Domain The collection of all input values. The
domain here would be 0, 1, 2, 3, and 4. Range
The collection of all output values. The Range
here would be 1, 3, 5, 7, and 9.
A
B
0 1 2 3 4
1 2 3 4 5 6 7 8 9
Domain (x variable) Range (y variable)
Input-Output Table
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Function, Function, Which one is a Function??
Domain? Range?
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Lets talk about .Functions!!

• Functions can be described in four ways

Graph
Equation
With Words
Input-Output Tables
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One way to tell if a graph is a function is the
vertical line test, which says if it is possible
for a vertical line to meet a graph more than
once, the graph is not a function.  The figure
below is an example of a function.

Is a straight line a function?
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Lets Practice

• Write an input-output table for the function
• y 6x 5 .
• Use the numbers 1, 2, and 3 as the domain.
• Then graph the line on a coordinate plane and
  check to see if it is a function.
• Now try y x
• .5

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In words

• A drive through safari charges 5 admission per
  car and 1.25 admission for each person in the
  car. The total cost C at the safari is given as
  C 5 1.25n, where n represents the number of
  people in the car. (Assume a maximum of 7 people
  can fit in a car).
• Make an input-output table.
• List the domain and range.
• Is this equation a function?
• Graph the points as a line on a coordinate plane.

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Homework!

Textbook page 50 20-32 even
Please remember to bring your textbook home and
bring it to class tomorrow.
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Since we have extra time

• Lets see who was listen and take a..

Functions Pop -Quiz