What is Signum Function Video Lecture | Additional Study Material for Class 12

now we have the sixth function to learn
that's called Signum function and it's
really really important and a short but
very very important because I've seen in
examination being asked what is the
definition of Signum function all right
so a function can be defined something
like this you know whenever a function
is defined from a real number two real
number and the domain of that function
first I'm writing if the domain of the
function is all possible real number but
you are getting restricted in range
range is only minus 1 0 and 1 then that
time such a function is called Signum
function all right I'm going to say f of
X is something like 1 0 and minus 1
right if X is greater than 0 if X is
equals to 0 and if less than 0 all right
so domain is possible everything you can
put - 1 - 2 - 3 - hundred - mm -
millions and billions whatever you put
here but the result will be 1 and minus
1 and 0 all right
and if you're putting you know in a
number line ever the value you're
putting whatever the positive number any
bigger number whatever you put in for
all you know if you are putting 1 let's
say if you put your 1 you'll get your 1
because 1 is greater than 0
so you'll get here all right and
similarly if you put here 2 let's say 2
is greater than 0 so again you'll get 1
you know if you put here let's say 4
again you'll get here 1 if you put in
anything number let's say billions or
whatever you know again you'll get here
1 alright and in the same way if you put
here 0 alright if you put in 0 then
you're going to get 0 so if you put 0
you'll be out here you know only so if
you put any a let's say minus 1 if you
put here minus 1 what you gonna get
minus 1 is less than 0 so you're gonna
get again - 1 year so if you put minus 1
you'll get this is minus 1 let's see
yeah all right and if you put here let's
say minus 2 then again you will get 2
minus 1 all right if you put your minus
3 you again minus minus 1 because these
all numbers these all numbers are less
than 0 so what do you were you putting
let's say - Trillian you put then again
you'll get minus 1 so you
Graff will be something like this
posting once I get this right and lately
once something like this right this is
your graph of the signal function and
then let me clear you one thing this at
zero you'll get zero all right
but at zero you cannot get anything here
you cannot get positive one and A zero
you kind of get negative one so keep in
mind this is back end all right this is
void there is nothing and after a livin
a single bit if you move you'll get a
straight three straight line and
similarly negative number if you put
anything you'll get like this so this is
the graph of the signal function alright
and you know as the product is always
output is always one and one you know
like if you have P air and you divide P
then you'll get one all right and if you
have P and you divide by minus P then
you'll get minus one so always your
output is either one or negative one
I'm leaving for a while zero so you know
this signal function can be written
something something like this you know
in the way of absolute value also
because always you know you're getting
one so it's gonna be like ratio of
absolute value of x it's always in the
numerator you're getting positive number
and in the denominator you just writing
X right this will always result you you
know and there is one condition X can
never be zero if X is zero you know that
time you'll get some undetermined value
and 4x and 4x you'll get always zero
okay so this is also can be defined as a
as a signal function alright for example
let's say I'm taking X as a -3 for
awhile then what I will get here you can
guess it easily all right when I'm
putting f as a negative 3 then I will
get here absolute value of minus 3
divided by minus 3 all right this is X
so absolute value of negative 3 you will
get positive 3 divided by minus 3 so
you're going to get 3 3 cancel and
you'll get minus 1 so the result is
minus 1 and say if you put here 3 all
right if you put here 3 then you're
going to get here again absolute value
of 3 divided by 3 so you're going to get
3 by 3 that's 1 again so you get 2 minus
1 on 1 and if you put 0 I told you if X
is not equal to 0 this is
X is not equals to 0 and for x equals to
0 if you are putting X as a zero then
you will get 0 so minus 1 1 or 0 what
about number you put if you put your
hundred also you'll get 100 over 100 and
you will get minus 1 if you put here
again one hundred two thousand whatever
you will always get these three numbers
always in all ways