Video Transcript
Mapping Diagrams: Domain and
Range
This is a mapping diagram. So what a mapping diagram means is
if we have every value in set A, we can transform it to give us every value in set
B. Now in this case if we take two and
we add four, we get six; if we take four and we add four, we get eight. So then the last one, we have 𝑥
and we add four, we get 𝑥 and four. Now 𝑥 add four: so it’s obviously
it would be a graph if we said 𝑦 equals 𝑥 add four. So I’ll show you how Cartesian
graph is actually exactly the same as one of these mapping diagrams.
So this is the graph of 𝑦 equals
𝑥 add four. Now let’s look at our input
values. So, in our mapping diagram, if we
input two, then we receive six. So, in the graph, if we input two,
then you receive six. And in our mapping diagram, if we
input four, we receive eight. And then in our graph, if we input
four, we receive eight. Now these input and these output
values have two very special names. So the input values are called “the
domain.” So think about that domain. And our domain will always
represent the 𝑥-axis. And then the output values are
called “the range.” And the range will always represent
the 𝑦-axis. Or if we take it back to our
mapping diagram, we’re saying the domain are our input values or the values in set
A. And then the range are our output
values or the values in set B. Now this is relatively simple:
putting one value in, you get one value out. So let’s look at another
example.
Okay taking a second to look at
this example, we can see the thing that’s different here is that there are two input
values giving us just one output value. So we would call this “a
many-to-one function.” Now in this case if we have minus
one, what do we have to do to it to get one? We would have to times it by minus
one. So this is saying everything on the
left-hand side, all of the input values, we will have to square to get the output
values. So 𝑥 will then become 𝑥
squared. And again the input, the domain,
and then the output will be the range. Now let’s have a look at this
Cartesian graph as well to really understand it.
So this is our Cartesian graph. And we can see how it relates to
the mapping diagram. So if we input minus one in the
mapping diagram, we get one. And same if we input one, we also
get one. So in the graph if we input minus
one, we get one. And same if we input one, we also
get one. Now looking at minus two: if we
input minus two, we get four. And also if we input two, we get
four. So that tells us that two values in
the domain give us one value in the range. And again domain is the values you
put in — domain the 𝑥-axis — and the range will be the 𝑦-axis.
So in summary, this is a mapping
diagram where we input some value into set A and it gives us some value in set
B. And we always have to transform it
in the same way. So in this case, what we’ve done is
we transformed set A by adding two each time. So then 𝑥 would be 𝑥 add two. And the other important thing we
learnt in this video is the domain and range. So we learnt the domain, they’re
our input values and that’s always the 𝑥-axis. And the range are our output values
and that’s always the 𝑦-axis.
