Domain and range of a relation | Functions and their graphs | Algebra II | Khan Academy
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Domain and range of a relation | Functions and their graphs | Algebra II | Khan Academy


Determine the domain and range
for the relation described by the table. And so what they
want us to say, what they want us to figure out,
when they say the domain, they’re saying, what are all
of the possible inputs that we could put into– in
this case, a relation, and later we’ll see into
functions– and so over here– or I guess one way
to think about it– what are all of the inputs
that this relationship is defined for? And so you can view
the x as the input. So when x is negative 1, y is 3. When x is 3, y is negative 2. When x is 3 again, now y is 2. And that’s why we can’t
describe this as a function here, because we have two
different y values for a given x value, but it
can be a relation. When x is 4, y is 8. When x is 6, y is negative 1. So to answer the
first part, when they ask us what is the domain
of this relation, they’re really just saying,
what are all the inputs? What are all the x values for
which this relation is defined? And they list the x
values right over here. So it is the set– and that’s
what these curly brackets mean that I’m about to
describe a set– it is a set of the numbers,
negative 1, 3, 4, and 6. So all we’re saying
here is if we say the domain of this
relation is these four numbers, it says that this
relation is defined for any of these four numbers. If you give any of these
four numbers as an x value, there is a y, at least one
y value, associated with it. Now, when they talk about
the range of this relation– and the idea also
applies to functions, which are a more specific
class of relations. You can view them as a
well-behaved relation. The range is, what are
all the possible outputs that this relation can give you? Or given the inputs, what are
all of the possible values that this relation can take on? So here you’ll take a look at
all of the possible y values that it can take on. So we can get– and I’ll write–
we could write them in order or we don’t have to
write them in order, but I’ll write them in order
just for the sake of it. Actually, let’s just
go straight this way. It doesn’t have to be in order. A set does not imply
some type of order. It just means a
collection of things. So the range here, well, our y
value can take on the value 3. It can take on the
value negative 2. It can take on the value 2. It can take on the value 8. And it can take on
the value negative 1. And we’re done. These are the x values for
which this relation is defined that you can actually find an
association or relationship. And these are all the y values. These are all of the outputs of
the relation that it can take on, and we just looked right
over here to find them.

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