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Relation and Function | Darwin Ong | YouTubeToText
YouTube Transcript: Relation and Function
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[Music] [Applause]
[Applause] [Music]
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
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
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
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
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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