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Domain and range 2 | Functions and their graphs | Algebra II | Khan Academy


We are asked to represent the
following function on the coordinate plane. And they give us domain, and
then they give us a range, a set of values that our
function can take on. And the way the question has
been phrased, I’m assuming they assume that the negative 8
maps to the 4, the negative 6 maps to the 3, the negative 4
maps to the 2, the negative 2 maps to 1, and the
0 maps to 0. Because you could have another
function with this exact same domain, and this exact same
range, where the mapping is different, where negative
8 maps to 3, and negative 6 maps to 4. So this domain and this
range could be for many different functions. But when they say represent the
following function, I’m assuming that they want us to
assume that they’re kind of in order, the pairing. So let’s just graph this
function, or represent it using their terminology. So let me draw some axes here. So this is the domain, the
independent variable, just like that, often known as the
x-axis or the horizontal axis. And all of our domain, all of
the values, these are all non-positive numbers, so let
me give a lot more space to quadrant II. All of our range are
positive numbers. They’re going to be hanging out
in the top left quadrant, or quadrant II, just
like that. And the values that my domain
can take on are 0 through negative 8, and every even
negative number. So it’s 0, let me do it like
this, so 0 is there. And then we have negative 2,
negative 4, negative 6, and then we have negative
8 just like that. And then our range goes
from 0 through 4. So this is 0, then you have 1,
then you have 2, then you have 3, and then you have 4. So if we assume the mapping,
that if you give this function a negative 8, it’s going
to map to 4, then we can plot it here. So if we take this first pair
right there, you give me a negative 8, this function
is going to give me a 4. So negative 8, 4 is that
point right there. So if you imagine that this is
the x-axis, this would be the f of x axis, if we’re assuming
that f is this function. You give me a negative
6, I’ll give you a 3. Negative 6 and 3. You give me a negative 4, this
function will pop out a 2. Negative 4 comma 2. And then you give a negative
2, this function will pop out a 1. F of negative 2 is 1. And then finally, f of 0 is 0. So we’ll just plot
it right there. So that’s the function. I’ve represented it. And remember, I just assumed
that negative 8 maps to 4, negative 6 maps to 3, but you
could have multiple functions that have this domain
and range. But just the way that they said
the following function, I’m assuming this is what
they want us to do.

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