Okay, in this video, I just wanna finish off kind of the general vertical and
horizontal stretching and reflecting.
In this one, I'm gonna talk about reflecting, and
so what we're gonna look at are conditions 5 and 6 here.
The idea is, if you basically plug a big O negative sign out in front of
your formula, it's gonna reflect your graph about the x-axis.
If you replace all of your x's with -x's, so, you kinda change, well,
not necessarily change the sign, you're gonna reflect about the y-axis.
So kind of generally, again.
So this will be probably the easiest of all of them, kind of a general,
just again, a general idea.
Again, if the negatives on the outside, it flips it about the x-axis.
And if you think about it, I mean, that really makes sense.
I mean, what's gonna happen?
You plug x in, you get some y value out.
That's what f(x) is, okay?
So suppose it was positive originally.
Well, if you plug a negative out front, what's it gonna do?
It's going to change the sign and reflect it down to the other side.
So, really that's what it's doing.
The negative out front changes the sign on all the y values,
and that has the effect of reflecting it about the x-axis.
Likewise, if it's on the inside.
[COUGH] You reflect the graph about the y-axis.
And now, the idea is, whatever you plugged in for 2 originally,
you're gonna get that same output at now -2, and
that's gonna have the effect of shifting it about the y-axis.
So just a quick little graph.
Let's graph, y equals negative f(x), here real quick.
So again, all it does is, it kinda preserves its sort of general shape.
All that happens is, again, you're just flipping it.
So instead of this first little salt used part.
It's now instead of going up, it's gonna go down To -2..
So there's the original part that was up is now down.
This original part that was down, will now go up, okay?
So again, a very loose graph on these two.
And instead of being down here at (-1,2), again,
now if that point flips, it's gonna be up here +1, and
it will extend over a distance of 2 units.
And then if this portion down here that was at (2,-2)
we will now flip up to the top, and be up here at 2 and
it'll extend over a distance of 4 units.
Okay, so that's the graph of y equals negative f of x.
Again, all it does is, stuff that was above the x-axis
gets flipped below on the x-axis and vice versa, okay?
So, Let's do the other one here real quick.
So again, very general, I'm gonna do some more kinda
concrete ones with functions that you probably encountered,
and produce some other graphs as well.
Just the general idea here.
Okay, last but not least, again we said, if the negatives on the inside all
that does is reflects a the graph about the x-axis.
So now this portion that was originally on the left side is gonna
get moved over to the right side.
Okay, there's my little arrow, and
this portion that was on the bottom will get moved over to the left side.
So, if- Instead of going over from 0 to -2,
if you reflect it, it'll go over from 0 to 2, and
it'll still go up and then back down, up here to height of 2.
And then if you think about the other part, it was going down from -2 to -4.
So now, it'll go down and come back up between +2 and +4, okay?
And lastly, the part that was on the right side, well,
instead of going to the right like it normally did, if it reflects,
it'll now point over to the left.
And then we'll extend over to an x coordinate of negative 2,
and then we'll jump down here, and we'll extend over until we get to negative 4.
Okay, so again, this is supposed to be a flat little line,
very sloppy little graph.
But again, the idea is the shape is exactly preserved.
The only thing that happens is you're just reflecting.
I mean, basically, if you have this on a piece of paper,
just turn your paper over, okay?
And that new graph that you see, is gonna be f of negative x, okay?
So, that's what the new graph will look like, all right?
So I hope these help.
Again, I'm gonna put all of this together, the all the stretching and
reflecting and shifting and transforming with some different graphs,
maybe trig functions, exponential functions, x squared absolute value of x.
Do all that in another video.
So, feel free to dig around for that as well.