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Current time:0:00Total duration:3:16

CCSS Math: HSF.BF.B.3

- [Voiceover] G of x is a
transformation of f of x. The graph here shows this
is y is equal to f of x, the solid blue line, This is y is equal to g
of x as a dash red line. And they ask us, "What is
g of x in terms of f of x?" And like always, pause the
video and see if you can give a go at it and then
we're going to do it together. All right, so when you
immediately look like it, it looks like g of x is kind of
a thinned-up version of f of x. It seems like if you were to compress it to towards the center,
that's what g of x looks like but let's put a little bit
more meat on that bone and see if we can identify
corresponding points. So for example, if we were to
look at f of negative six. That's, so f of negative six. That seems like it corresponds
or it gives us the same value as f of negative six. So we wanna find the corresponding points. We hit this minimum point. We're coming back up. Hit the minimum point. We're coming back up. It seems like the corresponding
point right over there is g of negative three. So let's write that down. Let's see, it looks like f of negative six and it is equal to g of negative three. These are corresponding points. If you apply the transformation
at the point f equals, at the point negative six
comma f of negative six. You get to the point negative
three, g of negative three right over there. Let's do a couple of more. If you look at f is, so f of two, looks like it corresponds to g of one, f of two corresponds to g of one. So let's write that down. F of two looks like it
corresponds to g of one. And once again, I'm looking
at the where the functions hit the same value and also
optically I'm just looking at, well, looks like it's the
same part of the function if we assumed g of x is a
squeezed version of f of x. And so in general, it looks like for given x. So we could say f of x
is going to be equal to g of, well whatever you have it here, it seems like we have
half the value over here. So g of x over two. Or if you wanted to think of it the other way, if you want to think of the other way, if you want to say g of x is going to be f of... Well, whatever we have here, it's f of twice that. So f of two x. And we see that that
is one of the choices. The g of x is equal to f of two x. Whatever the x that you input into g of x, you get that same value
out of the function when you input two times that into f of x. These seem to validate that. It looks optically like that and we shrunk it down. One way to think about it when you take, when you multiply the
input into a function by a number larger than one, it's going to compress. It's going to make things happen faster. The input to the function
is going to increase or become negative faster so it thins it up. And if that doesn't make intuitive sense, you can also just try
some of these values. And I encourage you to try more. Find the corresponding points where the f's and the
g's seem to match up. And you'll see over and over again that to get the same value, you have to put two times as much into f as you have to put into g. Hopefully that helps.