Name: Scaling functions horizontally: examples | Transformations of functions | Algebra 2 | Khan Academy
Uploaded: 2020-03-27T17:41:07.000Z
Duration: 8 min 9 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Instructor] We're told this is the graph of function f,

Function g is defined as g of x is equal to f of two x.

So pause this video, and try to figure that out on your own.

and then I'll have a, well, actually just put g of x column.

And of course, g of x is equal to f of two x.

and actually let me see, when x is equal to,

I could pick a point like x equaling zero,

so g of zero is going to be f of two times zero.

which is going to be equal to a little bit over four,

And so they're going to both have the same y-intercept,

but interesting things are going to happen the further

or as our x increases in either direction away,

or as our x gets bigger in either direction from zero.

So let's think about what's going to happen

g of two is going to be equal to f of two times two,

two times two, which is equal to f of four.

So g of two is equal to f of four, which is equal to zero.

So notice, the corresponding point has kind of

gotten compressed in or squeezed in or squished in,

is everything's happening a little bit faster.

So this side of the graph is going to look something,

try to draw it a little bit better than that,

And what happens when you go in the negative direction?

Well, think about what g of negative two is.

G of negative two is equal to f of two times negative two,

So whatever was happening at x equals four

Whatever is happening at x equals negative four

is now going to happen at x equals negative two.

And I saw that we were at very clear points

at x equals negative four and x equals four on f,

It's going to look like it's been squished in

So now they've not only given the graph of f,

So pause this video, and try to figure that out.

All right, the key is to figure out the relationship

And what we can see, the main difference is,

is instead of an x here in f of x, we have an x over two.

So another way of thinking about it is g of x

is equal to f of not x but f of x over two.

Or another way of thinking about it, g of x

And then we can do a similar type of exercise.

And they've given us some interesting points,

or the point x equals two, the point x equals four,

Last time, when it was g of x is equal to two x,

Now things are going to happen half as fast.

are the ones that if I take half of them,

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Scaling functions horizontally: examples | Transformations of functions | Algebra 2 | Khan Academy

equivalent

figure

stretch

expression