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Relation and Function

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we have the relation

and functions but do not forget to

subscribe in my youtube channel

but that is updated my lecture is

nothing okay but i'm sad

so animals imitably in a relation

a relation is any set of ordered where

the set of all the first coordinate

is called the domain so you know first

coordinate in the adding domain

of the relation and the set of the all

the second coordinates is called the

grades so you first

coordinates in domain the second

coordinate you know adding green so

for example we have sets

of one three negative four two ten and

will be 1 negative 4 10 and

7. next

arrange arrange here our

range is 3 2 8 and

next slide so we have example here now

one three five

six seven it's not a relation because

it's not a set of ordered pairs

young set of two three and sets of four

and five

is a not religion

it's not a relation but just a set of

you want four two

five three and six and

it's a relation bucket because

one two three and then ring saturn is

is just a set of pair is that is

just a set of pairs of sets divide you know

know relation

one four two five three six are relation

so it's a relation or relation i mean

okay so the domain is one two three and

then the range is four

y transpose habit line x will be

negative one

so much substitute time value if x is zero

zero

our y is one if x is one

and then our y is zero if x

is two r y is

negative one if x

is three r y is negative two

okay if x is four

r y is negative three and then

if x is negative one our y is

positive two if x is negative two our y

so yeah it's nothing orders it so we

have zero one

one zero two negative one three

negative two four negative three one

negative one and two

value in the same seconds x that's all

nothing valuable

sorry so then

so the graph which shows points on the

cartesian coordinates plane can be

thought of a set of ordered pairs so we

have withdrawal

nothing else negative two negative three

negative one negative two pi

one three and zero and one so it's

adding pair of sets so

hence the graph is a

graph of relation and

our domain is negative two

negative one two one and

zero our range is

okay so we have z uh sets of zero zero

one and one one negative one four two

four and negative three but in the

mushroom this is a

okay so and dominating zero one mayweather

next a function

is a relation in which

so first for every first score z

there is exactly one second coordinate check

is a relation is a functions so follower

for every first element of x there are correspond

correspond

a unique second element of y

note every function is a relation

so for example is the given is the

relation given by the sets

of ordered pairs shown below a function

negative two zero and three

seven we have two

okay so determine whether which of the

following relations

on x so six negative one

negative seven five eight

and also the check not in the data

domain now

lipa so it means a function

on x eleven zero

representations of a function so a

function can be represented by using

a table of values or a set of ordered pairs

pairs

or numbers by mapping by picture of

graph by equation

and by rule of correspondence expressed

in words

so for example edison

is a working student he works in mount doming's

doming's

restaurant so as a waiter he earns pesos

a working student so represents

the earning of edison as a function of rs

he works okay so table of values

we have number of rs and earnings

13 14 15 and 16 hours

so 10 11 12 13 14 15 and 16

hours okay so but another

13 1040 14 1 120

and then 15 1 200 001 2

and then sixteen is one to eighty so

january and sets of order

pairs okay panoramic mapping so sabjan

we have

one to one correspondence each element in

x or h pairs with only one element

okay next condition many to one correspondence

correspondence

or many or more than one numbers in x pairs

pairs

for example one negative one two

negative two

three negative three four negative four

five and negative five

so similar one four nine

and ten okay eleven okay so jan

negative one occurrence of one the

current this is

one two negative two

negative three sub three and negative four

four

and this is four and so it's a negative five

five and

one number in expired with the different

number in y for

a one-to-one correspondence and

many-to-one the correspondence are

called functions while the one-to-many resp

resp

so rules are correspondences for us in

words and equations so

the total total earning of arizona is 80

times the number of rs he worked so divide

divide

e represent the total earnings of edison

while h is the hours of he work or

number of rc work

so e is equal to times h or 80 times h

okay so we have the testing of functions

so the following characteristic characteristic

characteristic

of a function will help us decide when

we test for a function when two sets of

numbers or figures are given

each element in x must be matched with an

element in y times

so some elements in y may not be much

with any element in x and then lastly we

have two or more elements in x

so for example to let x or

sets of one two three and says a b c d

e so determine which of the following

sets are of ordered pairs or

figures represent a function from

x set x x to set y

okay check nothing

so they have example one a

two a c three or passing b

okay so we have the x and y so one two three

three

so a b c d e and okay

more than one number x with the same

number in y

so you know i think that so i'm not

so one too many corresponds

correspondence one member in experience

with the different number in y or diva

so we have to determine which of the

following equations represents

minus x squared plus one so obtaining

that interest potential d by y is equal to

x squared that's the result of the

positive n minus one

something or else we can

use the function of x is equal to x

y squared plus 1 is equal to x and

so x y

represents a function if and only if a

vertical line

intersects the graph at most once

can following grubs can be graphs of functions

using my youtube channel so my name is

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