[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.26,Default,,0000,0000,0000,,Okay, in this video, I just wanna finish\Noff kind of the general vertical and
Dialogue: 0,0:00:04.26,0:00:06.57,Default,,0000,0000,0000,,horizontal stretching and reflecting.
Dialogue: 0,0:00:06.57,0:00:09.98,Default,,0000,0000,0000,,In this one,\NI'm gonna talk about reflecting, and
Dialogue: 0,0:00:09.98,0:00:13.80,Default,,0000,0000,0000,,so what we're gonna look at\Nare conditions 5 and 6 here.
Dialogue: 0,0:00:13.80,0:00:18.61,Default,,0000,0000,0000,,The idea is, if you basically plug\Na big O negative sign out in front of
Dialogue: 0,0:00:18.61,0:00:23.28,Default,,0000,0000,0000,,your formula, it's gonna reflect\Nyour graph about the x-axis.
Dialogue: 0,0:00:23.28,0:00:28.70,Default,,0000,0000,0000,,If you replace all of your x's with -x's,\Nso, you kinda change, well,
Dialogue: 0,0:00:28.70,0:00:34.31,Default,,0000,0000,0000,,not necessarily change the sign,\Nyou're gonna reflect about the y-axis.
Dialogue: 0,0:00:34.31,0:00:37.89,Default,,0000,0000,0000,,So kind of generally, again.
Dialogue: 0,0:00:37.89,0:00:41.50,Default,,0000,0000,0000,,So this will be probably the easiest\Nof all of them, kind of a general,
Dialogue: 0,0:00:41.50,0:00:43.04,Default,,0000,0000,0000,,just again, a general idea.
Dialogue: 0,0:00:43.04,0:00:46.48,Default,,0000,0000,0000,,Again, if the negatives on the outside,\Nit flips it about the x-axis.
Dialogue: 0,0:00:46.48,0:00:49.05,Default,,0000,0000,0000,,And if you think about it,\NI mean, that really makes sense.
Dialogue: 0,0:00:49.05,0:00:50.67,Default,,0000,0000,0000,,I mean, what's gonna happen?
Dialogue: 0,0:00:50.67,0:00:54.20,Default,,0000,0000,0000,,You plug x in, you get some y value out.
Dialogue: 0,0:00:54.20,0:00:56.44,Default,,0000,0000,0000,,That's what f(x) is, okay?
Dialogue: 0,0:00:56.44,0:00:58.84,Default,,0000,0000,0000,,So suppose it was positive originally.
Dialogue: 0,0:00:58.84,0:01:01.47,Default,,0000,0000,0000,,Well, if you plug a negative out front,\Nwhat's it gonna do?
Dialogue: 0,0:01:01.47,0:01:04.82,Default,,0000,0000,0000,,It's going to change the sign and\Nreflect it down to the other side.
Dialogue: 0,0:01:04.82,0:01:07.09,Default,,0000,0000,0000,,So, really that's what it's doing.
Dialogue: 0,0:01:07.09,0:01:12.02,Default,,0000,0000,0000,,The negative out front changes\Nthe sign on all the y values,
Dialogue: 0,0:01:12.02,0:01:16.98,Default,,0000,0000,0000,,and that has the effect of\Nreflecting it about the x-axis.
Dialogue: 0,0:01:16.98,0:01:18.98,Default,,0000,0000,0000,,Likewise, if it's on the inside.
Dialogue: 0,0:01:18.98,0:01:22.74,Default,,0000,0000,0000,,[COUGH] You reflect\Nthe graph about the y-axis.
Dialogue: 0,0:01:22.74,0:01:27.96,Default,,0000,0000,0000,,And now, the idea is,\Nwhatever you plugged in for 2 originally,
Dialogue: 0,0:01:27.96,0:01:31.96,Default,,0000,0000,0000,,you're gonna get that same\Noutput at now -2, and
Dialogue: 0,0:01:31.96,0:01:36.100,Default,,0000,0000,0000,,that's gonna have the effect of\Nshifting it about the y-axis.
Dialogue: 0,0:01:36.100,0:01:38.48,Default,,0000,0000,0000,,So just a quick little graph.
Dialogue: 0,0:01:38.48,0:01:42.41,Default,,0000,0000,0000,,Let's graph, y equals negative f(x),\Nhere real quick.
Dialogue: 0,0:01:47.64,0:01:53.02,Default,,0000,0000,0000,,So again, all it does is, it kinda\Npreserves its sort of general shape.
Dialogue: 0,0:01:53.02,0:01:56.08,Default,,0000,0000,0000,,All that happens is, again,\Nyou're just flipping it.
Dialogue: 0,0:01:56.08,0:01:59.73,Default,,0000,0000,0000,,So instead of this first\Nlittle salt used part.
Dialogue: 0,0:01:59.73,0:02:08.15,Default,,0000,0000,0000,,It's now instead of going up,\Nit's gonna go down To -2..
Dialogue: 0,0:02:08.15,0:02:11.16,Default,,0000,0000,0000,,So there's the original part\Nthat was up is now down.
Dialogue: 0,0:02:11.16,0:02:17.86,Default,,0000,0000,0000,,This original part that was down,\Nwill now go up, okay?
Dialogue: 0,0:02:17.86,0:02:20.64,Default,,0000,0000,0000,,So again, a very loose graph on these two.
Dialogue: 0,0:02:20.64,0:02:25.28,Default,,0000,0000,0000,,And instead of being down here at (-1,2),\Nagain,
Dialogue: 0,0:02:25.28,0:02:29.91,Default,,0000,0000,0000,,now if that point flips,\Nit's gonna be up here +1, and
Dialogue: 0,0:02:29.91,0:02:33.41,Default,,0000,0000,0000,,it will extend over a distance of 2 units.
Dialogue: 0,0:02:33.41,0:02:39.14,Default,,0000,0000,0000,,And then if this portion\Ndown here that was at (2,-2)
Dialogue: 0,0:02:39.14,0:02:44.17,Default,,0000,0000,0000,,we will now flip up to the top,\Nand be up here at 2 and
Dialogue: 0,0:02:44.17,0:02:48.38,Default,,0000,0000,0000,,it'll extend over a distance of 4 units.
Dialogue: 0,0:02:48.38,0:02:52.20,Default,,0000,0000,0000,,Okay, so that's the graph of\Ny equals negative f of x.
Dialogue: 0,0:02:52.20,0:02:56.65,Default,,0000,0000,0000,,Again, all it does is,\Nstuff that was above the x-axis
Dialogue: 0,0:02:56.65,0:03:01.21,Default,,0000,0000,0000,,gets flipped below on the x-axis and\Nvice versa, okay?
Dialogue: 0,0:03:01.21,0:03:07.23,Default,,0000,0000,0000,,So, Let's do the other\None here real quick.
Dialogue: 0,0:03:12.82,0:03:17.52,Default,,0000,0000,0000,,So again, very general,\NI'm gonna do some more kinda
Dialogue: 0,0:03:17.52,0:03:22.95,Default,,0000,0000,0000,,concrete ones with functions\Nthat you probably encountered,
Dialogue: 0,0:03:22.95,0:03:26.34,Default,,0000,0000,0000,,and produce some other graphs as well.
Dialogue: 0,0:03:26.34,0:03:28.34,Default,,0000,0000,0000,,Just the general idea here.
Dialogue: 0,0:03:33.14,0:03:38.08,Default,,0000,0000,0000,,Okay, last but not least, again we said,\Nif the negatives on the inside all
Dialogue: 0,0:03:38.08,0:03:41.50,Default,,0000,0000,0000,,that does is reflects\Na the graph about the x-axis.
Dialogue: 0,0:03:41.50,0:03:46.36,Default,,0000,0000,0000,,So now this portion that was\Noriginally on the left side is gonna
Dialogue: 0,0:03:46.36,0:03:48.94,Default,,0000,0000,0000,,get moved over to the right side.
Dialogue: 0,0:03:50.50,0:03:52.38,Default,,0000,0000,0000,,Okay, there's my little arrow, and
Dialogue: 0,0:03:52.38,0:03:55.92,Default,,0000,0000,0000,,this portion that was on the bottom\Nwill get moved over to the left side.
Dialogue: 0,0:03:55.92,0:04:00.66,Default,,0000,0000,0000,,So, if- Instead of going\Nover from 0 to -2,
Dialogue: 0,0:04:00.66,0:04:05.77,Default,,0000,0000,0000,,if you reflect it,\Nit'll go over from 0 to 2, and
Dialogue: 0,0:04:05.77,0:04:11.96,Default,,0000,0000,0000,,it'll still go up and then back down,\Nup here to height of 2.
Dialogue: 0,0:04:11.96,0:04:17.62,Default,,0000,0000,0000,,And then if you think about the other\Npart, it was going down from -2 to -4.
Dialogue: 0,0:04:17.62,0:04:24.42,Default,,0000,0000,0000,,So now, it'll go down and\Ncome back up between +2 and +4, okay?
Dialogue: 0,0:04:24.42,0:04:28.52,Default,,0000,0000,0000,,And lastly,\Nthe part that was on the right side, well,
Dialogue: 0,0:04:28.52,0:04:33.48,Default,,0000,0000,0000,,instead of going to the right like\Nit normally did, if it reflects,
Dialogue: 0,0:04:33.48,0:04:36.02,Default,,0000,0000,0000,,it'll now point over to the left.
Dialogue: 0,0:04:36.02,0:04:41.44,Default,,0000,0000,0000,,And then we'll extend over to\Nan x coordinate of negative 2,
Dialogue: 0,0:04:41.44,0:04:48.74,Default,,0000,0000,0000,,and then we'll jump down here, and we'll\Nextend over until we get to negative 4.
Dialogue: 0,0:04:48.74,0:04:53.10,Default,,0000,0000,0000,,Okay, so again,\Nthis is supposed to be a flat little line,
Dialogue: 0,0:04:53.10,0:04:55.12,Default,,0000,0000,0000,,very sloppy little graph.
Dialogue: 0,0:04:55.12,0:04:59.34,Default,,0000,0000,0000,,But again, the idea is\Nthe shape is exactly preserved.
Dialogue: 0,0:04:59.34,0:05:01.94,Default,,0000,0000,0000,,The only thing that happens\Nis you're just reflecting.
Dialogue: 0,0:05:01.94,0:05:05.46,Default,,0000,0000,0000,,I mean, basically,\Nif you have this on a piece of paper,
Dialogue: 0,0:05:05.46,0:05:07.60,Default,,0000,0000,0000,,just turn your paper over, okay?
Dialogue: 0,0:05:07.60,0:05:13.68,Default,,0000,0000,0000,,And that new graph that you see,\Nis gonna be f of negative x, okay?
Dialogue: 0,0:05:13.68,0:05:16.58,Default,,0000,0000,0000,,So, that's what the new graph\Nwill look like, all right?
Dialogue: 0,0:05:16.58,0:05:17.46,Default,,0000,0000,0000,,So I hope these help.
Dialogue: 0,0:05:17.46,0:05:22.66,Default,,0000,0000,0000,,Again, I'm gonna put all of this together,\Nthe all the stretching and
Dialogue: 0,0:05:22.66,0:05:27.95,Default,,0000,0000,0000,,reflecting and shifting and\Ntransforming with some different graphs,
Dialogue: 0,0:05:27.95,0:05:33.86,Default,,0000,0000,0000,,maybe trig functions, exponential\Nfunctions, x squared absolute value of x.
Dialogue: 0,0:05:33.86,0:05:35.31,Default,,0000,0000,0000,,Do all that in another video.
Dialogue: 0,0:05:35.31,0:05:38.75,Default,,0000,0000,0000,,So, feel free to dig around for\Nthat as well.