0:00:00.000,0:00:04.262
Okay, in this video, I just wanna finish[br]off kind of the general vertical and

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horizontal stretching and reflecting.

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In this one,[br]I'm gonna talk about reflecting, and

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so what we're gonna look at[br]are conditions 5 and 6 here.

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The idea is, if you basically plug[br]a big O negative sign out in front of

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your formula, it's gonna reflect[br]your graph about the x-axis.

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If you replace all of your x's with -x's,[br]so, you kinda change, well,

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not necessarily change the sign,[br]you're gonna reflect about the y-axis.

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So kind of generally, again.

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So this will be probably the easiest[br]of all of them, kind of a general,

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just again, a general idea.

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Again, if the negatives on the outside,[br]it flips it about the x-axis.

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And if you think about it,[br]I mean, that really makes sense.

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I mean, what's gonna happen?

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You plug x in, you get some y value out.

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That's what f(x) is, okay?

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So suppose it was positive originally.

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Well, if you plug a negative out front,[br]what's it gonna do?

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It's going to change the sign and[br]reflect it down to the other side.

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So, really that's what it's doing.

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The negative out front changes[br]the sign on all the y values,

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and that has the effect of[br]reflecting it about the x-axis.

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Likewise, if it's on the inside.

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[COUGH] You reflect[br]the graph about the y-axis.

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And now, the idea is,[br]whatever you plugged in for 2 originally,

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you're gonna get that same[br]output at now -2, and

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that's gonna have the effect of[br]shifting it about the y-axis.

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So just a quick little graph.

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Let's graph, y equals negative f(x),[br]here real quick.

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So again, all it does is, it kinda[br]preserves its sort of general shape.

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All that happens is, again,[br]you're just flipping it.

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So instead of this first[br]little salt used part.

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It's now instead of going up,[br]it's gonna go down To -2..

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So there's the original part[br]that was up is now down.

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This original part that was down,[br]will now go up, okay?

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So again, a very loose graph on these two.

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And instead of being down here at (-1,2),[br]again,

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now if that point flips,[br]it's gonna be up here +1, and

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it will extend over a distance of 2 units.

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And then if this portion[br]down here that was at (2,-2)

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we will now flip up to the top,[br]and be up here at 2 and

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it'll extend over a distance of 4 units.

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Okay, so that's the graph of[br]y equals negative f of x.

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Again, all it does is,[br]stuff that was above the x-axis

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gets flipped below on the x-axis and[br]vice versa, okay?

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So, Let's do the other[br]one here real quick.

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So again, very general,[br]I'm gonna do some more kinda

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concrete ones with functions[br]that you probably encountered,

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and produce some other graphs as well.

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Just the general idea here.

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Okay, last but not least, again we said,[br]if the negatives on the inside all

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that does is reflects[br]a the graph about the x-axis.

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So now this portion that was[br]originally on the left side is gonna

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get moved over to the right side.

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Okay, there's my little arrow, and

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this portion that was on the bottom[br]will get moved over to the left side.

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So, if- Instead of going[br]over from 0 to -2,

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if you reflect it,[br]it'll go over from 0 to 2, and

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it'll still go up and then back down,[br]up here to height of 2.

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And then if you think about the other[br]part, it was going down from -2 to -4.

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So now, it'll go down and[br]come back up between +2 and +4, okay?

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And lastly,[br]the part that was on the right side, well,

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instead of going to the right like[br]it normally did, if it reflects,

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it'll now point over to the left.

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And then we'll extend over to[br]an x coordinate of negative 2,

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and then we'll jump down here, and we'll[br]extend over until we get to negative 4.

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Okay, so again,[br]this is supposed to be a flat little line,

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very sloppy little graph.

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But again, the idea is[br]the shape is exactly preserved.

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The only thing that happens[br]is you're just reflecting.

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I mean, basically,[br]if you have this on a piece of paper,

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just turn your paper over, okay?

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And that new graph that you see,[br]is gonna be f of negative x, okay?

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So, that's what the new graph[br]will look like, all right?

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So I hope these help.

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Again, I'm gonna put all of this together,[br]the all the stretching and

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reflecting and shifting and[br]transforming with some different graphs,

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maybe trig functions, exponential[br]functions, x squared absolute value of x.

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Do all that in another video.

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So, feel free to dig around for[br]that as well.