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Functions: Domain and Range

 
Transcripts:
 
0:05    Hi welcome to math minute my name is
0:08
Adam and today we're going to be
0:10
about domain and range here are the
0:12
definitions of domain and range and
0:14
domain is all possible X values well
0:17
range is all possible Y values so what I
0:20
have drawn here is a function mapping
0:23
now I may have talked about this a
0:25
little bit earlier in the first video
0:27
what is a function but let's talk about
0:29
it again this is the set of X values and
0:32
this is the set of Y values so there are
0:35
certain cases where it's not everything
0:37
you can think of that is the X values
0:39
and not everything you can think of as
0:41
the Y values so what we want to do is
0:43
find out what can we plug into our
0:45
machine if we're talking about the
0:47
Machine again if we have a pencil
0:48
machine like we talked about earlier we
0:50
can only put in wood blocks we put can't
0:52
put in a rubber ball and get out a
0:53
pencil it doesn't make sense so the
0:56
domain is what we can put in the range
0:58
is what we can get out so I have an
1:00
example right here in the equation and
1:01
this is the square root of x minus 1
1:03
there's two things that really stop us
1:07
so what we want to do when we're talking
1:09
about the main the very first thing is
1:11
thinking what can't I do what is a
1:14
problem in this equation and I have
1:16
those two cases right here we can't take
1:18
the square root of negative number and
1:20
we also can't divide by 0 so we won't
1:22
talk about this in this video but we are
1:24
talking about this specifically we know
1:28
that whenever is under the square root
1:30
sign has to be positive so what we can
1:33
say is X minus one has to be greater
1:36
than or equal to 0 we can tilt still
1:39
take the square root of 0 so let's
1:41
literally write down what I just said X
1:44
minus 1 must be greater than or equal to
1:47
0 X minus 1 is greater than or equal to
1:52
0 it's kind of kind of weird because a
1:55
lot of time what you think in your head
1:56
is what you need to write down on paper
1:58
so with domain this is exactly what we
2:00
need to do now in the last video we
2:03
talked about how to solve inequalities
2:04
we can treat this just like an equal
2:06
sign so we know that X has to be greater
2:10
than or equal to 1 we're just adding one
2:13
to each side so what this says is that X
2:16
must be greater than or equal to 1 now
2:19
what this is written as in terms of
2:21
domain
2:23
is one because we're including so we
2:25
have a closed bracket to infinity so our
2:30
domain is one to infinity we can have
2:37
anything so this set of values right
2:40
here is one to infinity ok now we want
2:47
to find out what the range is this is a
2:48
little bit tricky because we can't
2:50
have as much of a concrete idea or
2:53
method solving this we need to just
2:55
think what do we know about this
2:58
original equation what are the values we
2:59
can get out from it well let's just
3:01
think can we get a negative number out
3:03
of that no we can't taking the square
3:06
root of anything is always going to give
3:07
us a positive number now what we do know
3:10
is that these are the only possible
3:12
values we can use one to infinity so
3:14
let's start plugging something of some
3:16
of them in see if we can notice a trend
3:18
so if we plug one in we have the square
3:21
root of one minus one which is zero the
3:24
square root of 0 is 0 now if we plug in
3:27
the square root of two minus one this is
3:31
the square root of one which is one now
3:34
if we keep increasing let's just take
3:36
the square root of five minus one equals
3:40
square root of 4 which equals two so as
3:44
you've noticed as we've gone from 1 to 2
3:46
to 5 we get bigger and bigger so what we
3:49
know is that the smallest possible value
3:51
is zero and as we get bigger and bigger
3:54
we can go as high as we want because if
3:56
we took the square root of 1 million
3:59
minus one that's going to be a big
4:01
number and if we went just a little bit
4:03
farther the square root of 1 million in
4:05
one minus one that's even bigger than
4:07
that so what we're saying is that that
4:09
can go to infinity that can keep going
4:11
on forever so we know that our smallest
4:14
value is zero and we also know that we
4:17
can go on forever so the domain was one
4:21
to infinity and from that we can find
4:23
the range was 0 to infinity so those
4:28
were all through solutions so what we're
4:30
saying now is that for this function
4:32
square root of x minus 1 we can plug in
4:36
anything from one to infinity and our
4:39
total set of possible solutions is from
4:42
0 to infinity so this has been a quick
4:45
overview of domain and range domains a
4:47
little bit easier to solve you can have
4:49
a concrete method as you've seen it's a
4:50
lot of writing down what you're thinking
4:52
that's my method of you know solving
4:55
domain just write down what you think
4:56
and range you use what you know about
4:59
the domain to solve for the range so
5:01
this has been domain and range hopefully
5:03
it's been helpful and we'll see you next
5:04
time
 
Before studying and practising the unit "What is a function", you should watch the previous video and try doing next exercises! Good luck!                                                                                                                                                                                                                                                                                                                                                                     
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Short url:   https://clilstore.eu/cs/5183