Relations and Functions | General Mathematics | Grade 11

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[Music]

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hi class welcome back to our channel for

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this video discussion

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and about ebooks

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some functions and

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relations

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okay so define when nothing young

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relation

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a relation is any set of ordered pairs

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the set of all the x components

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of the ordered pairs is called the

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domain

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of the relation

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and the set of all the y components is

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called the range

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okay so if it's a bn a relation is a

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rule

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that relates values from a set of values

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called the domain

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okay to a second set of values called

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the range

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so whether nothing imagine domain

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is your adding input

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machine

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while syringe is

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so

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let's give the domain and range of the

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following relation for number one

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we have one three

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two four

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five seven and six comma eight

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x components of the ordered pairs

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okay

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so on only on we have one

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two

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five

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and six

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nahua

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while young range number

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is the set of all y components so you

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know

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we have seven

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then the sixth meron eight

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guys

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three four seven and eight

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so next number two

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so

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begin adding in domain and range

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again your adding domain is the set of

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all x components so you know

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numbers we have negative two negative

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one

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then multiply negative two so since mean

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negative two naught

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that is our y components so we have four

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one

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zero

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then five

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and last is your negative two

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okay so puerto ri nothing arranged guys

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human numbers are adding set from lowest

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to highest or highest lowest depending

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guys

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um

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a relation in which each member of the

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domain is paired to exactly one member

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of the range is called a function

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so on the banks of being none

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[Music]

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relation

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function

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if no two ordered pairs have the same x

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value but different

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y values

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function

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number one

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we have one two two three three four and

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four comma five

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so as you can see guys um

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input

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nothing is a function

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okay

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next number two

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we have one comma one

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then two comma two three comma three and

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four comma four

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so as you can see guys now you mean

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nothing is

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a unique output

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or is output so ebx bn young number to

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nothing is also a function

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okay

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next number three

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one zero

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zero one

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negative one zero and zero

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negative one

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okay

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so guys

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which is zero

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and zero

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domain is paired to exactly

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one member of the range so this time

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domain

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is

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okay which is one and negative one so

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therefore

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uh number three is not a function

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okay

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so next number four we have negative two

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four

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negative one one

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zero zero one one then two

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four

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okay

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so

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uh

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domain nothing which is negative two

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negative one zero one two is

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is a function

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guys

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okay next

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uh functions can also be represented

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through mapping

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okay so where the elements of the domain

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are map

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to the elements of the range using

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arrows okay so in this case

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uh the relation or function is

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represented by the set of all the

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connections

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by the arrows all right so try

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which of the following mapping

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diagrams represent function

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x component

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corresponds to a unique

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range tama young one corresponds to

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three two corresponds to five three

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corresponds to nine then four to seven

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then five to thirty three so latina

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input nathan is my unique output so

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therefore your number one nothing is a

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function

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okay so function n

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so next number two

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uh we have

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x

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u7 output near one you eat an output in

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a zero then your nine and output is zero

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all right so one problem guys

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okay

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so next number three naman

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meru

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11 13 17 19 and 23.

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so guys

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11 and

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13.

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okay then at the same time your input

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not in the two is made in the output

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output

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okay so this time

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uh your input not in the seven meet the

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level output so eb sub n

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uh this function or this relation is not

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a function

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all right nine indian but guys you're

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adding uh

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mapping diagrams

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okay so i unmoved dials of functions as

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a graph

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in the cartesian plane

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all right so given the graph of a

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relation we can easily identify if it is

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a function or not by using the vertical

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line test

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okay so underneath vertical line test

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a graph of a mathematical relation is

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said to be a function

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if any vertical line

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drawn passing through the graph

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touches the graph at exactly

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one point

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all right so if it's a bn

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uh magicking function is a graph if

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i connect in a vertical line

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that is

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example so which of the graphs

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represent a function

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so letter a

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so little guys are to test the graph

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again the gamma line of vertical line

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okay so um

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in a vertical line so any point in graph

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in your guys

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represents a function

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okay

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so next number two

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or letter b

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so determination is straight line

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so

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this line represents a function

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this ellipse is not a function or this

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graph is not a function

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so that means

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uh this graph represents a function

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um

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so that means this type of hyperbola is

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not a function

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and so gangnam language simply guys give

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me the new outing vertical line this

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so this is the end of our video i hope

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uh 19 day and you guys go on about ebay

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subscribe

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and if you have questions or

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clarifications kindly put them in the

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comment section below

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thank you guys for watching this is prof

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d i'll catch you on the flip side bye