[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.66,0:00:03.70,Default,,0000,0000,0000,,SALMAN KHAN: I'm here with\NJesse Roe of Summit Prep.
Dialogue: 0,0:00:03.70,0:00:04.78,Default,,0000,0000,0000,,What classes do you teach?
Dialogue: 0,0:00:04.78,0:00:07.04,Default,,0000,0000,0000,,JESSE ROE: I teach algebra,\Ngeometry, and algebra II.
Dialogue: 0,0:00:07.04,0:00:08.27,Default,,0000,0000,0000,,SALMAN KHAN: And now\Nyou're with us, luckily,
Dialogue: 0,0:00:08.27,0:00:10.24,Default,,0000,0000,0000,,for the summer, doing\Na whole bunch of stuff
Dialogue: 0,0:00:10.24,0:00:11.12,Default,,0000,0000,0000,,as a teaching fellow.
Dialogue: 0,0:00:11.12,0:00:12.66,Default,,0000,0000,0000,,JESSE ROE: Yeah, as\Na teaching fellow
Dialogue: 0,0:00:12.66,0:00:14.76,Default,,0000,0000,0000,,I've been helping with\Norganizing and developing
Dialogue: 0,0:00:14.76,0:00:17.29,Default,,0000,0000,0000,,new content, mostly on the\Nexercise side of the site.
Dialogue: 0,0:00:17.29,0:00:19.71,Default,,0000,0000,0000,,SALMAN KHAN: And the reason\Nwhy we're doing this right now
Dialogue: 0,0:00:19.71,0:00:23.02,Default,,0000,0000,0000,,is you had some very\Ninteresting ideas or questions.
Dialogue: 0,0:00:23.02,0:00:25.02,Default,,0000,0000,0000,,JESSE ROE: Yeah, so\Nas an algebra teacher,
Dialogue: 0,0:00:25.02,0:00:27.71,Default,,0000,0000,0000,,when I introduce that concept\Nof algebra to students,
Dialogue: 0,0:00:27.71,0:00:28.93,Default,,0000,0000,0000,,I get a lot of questions.
Dialogue: 0,0:00:28.93,0:00:30.47,Default,,0000,0000,0000,,One of those\Nquestions is, what's
Dialogue: 0,0:00:30.47,0:00:33.28,Default,,0000,0000,0000,,the difference between an\Nequation and a function?
Dialogue: 0,0:00:33.28,0:00:36.72,Default,,0000,0000,0000,,SALMAN KHAN: The difference\Nbetween an equation verses
Dialogue: 0,0:00:36.72,0:00:39.68,Default,,0000,0000,0000,,a function, that's an\Ninteresting question.
Dialogue: 0,0:00:39.68,0:00:42.14,Default,,0000,0000,0000,,Let's pause it and\Nlet the viewers
Dialogue: 0,0:00:42.14,0:00:43.60,Default,,0000,0000,0000,,try to think about\Nit a little bit.
Dialogue: 0,0:00:43.60,0:00:45.67,Default,,0000,0000,0000,,And then maybe we'll\Ngive a stab at it.
Dialogue: 0,0:00:45.67,0:00:46.67,Default,,0000,0000,0000,,JESSE ROE: Sounds great.
Dialogue: 0,0:00:49.34,0:00:51.32,Default,,0000,0000,0000,,So Sal, how would you\Nanswer this question?
Dialogue: 0,0:00:51.32,0:00:53.72,Default,,0000,0000,0000,,What's the difference between\Nan equation and a function?
Dialogue: 0,0:00:53.72,0:00:55.95,Default,,0000,0000,0000,,SALMAN KHAN: Let me think\Nabout it a little bit.
Dialogue: 0,0:00:55.95,0:00:56.66,Default,,0000,0000,0000,,So let me think.
Dialogue: 0,0:00:56.66,0:00:58.54,Default,,0000,0000,0000,,I think there's\Nprobably equations
Dialogue: 0,0:00:58.54,0:01:00.78,Default,,0000,0000,0000,,that are not functions\Nand functions that
Dialogue: 0,0:01:00.78,0:01:01.53,Default,,0000,0000,0000,,are not equations.
Dialogue: 0,0:01:01.53,0:01:03.57,Default,,0000,0000,0000,,And then there are probably\Nthings that are both.
Dialogue: 0,0:01:03.57,0:01:05.33,Default,,0000,0000,0000,,So let me think of it that way.
Dialogue: 0,0:01:05.33,0:01:08.17,Default,,0000,0000,0000,,So I'm going to draw-- if\Nthis is the world of equations
Dialogue: 0,0:01:08.17,0:01:12.56,Default,,0000,0000,0000,,right over here, so\Nthis is equations.
Dialogue: 0,0:01:15.31,0:01:19.46,Default,,0000,0000,0000,,And then over here is\Nthe world of functions.
Dialogue: 0,0:01:19.46,0:01:21.31,Default,,0000,0000,0000,,That's the world of functions.
Dialogue: 0,0:01:21.31,0:01:22.68,Default,,0000,0000,0000,,I do think there\Nis some overlap.
Dialogue: 0,0:01:22.68,0:01:25.52,Default,,0000,0000,0000,,We'll think it through\Nwhere the overlap is,
Dialogue: 0,0:01:25.52,0:01:26.72,Default,,0000,0000,0000,,the world of functions.
Dialogue: 0,0:01:26.72,0:01:29.05,Default,,0000,0000,0000,,So an equation that is not a\Nfunction that's sitting out
Dialogue: 0,0:01:29.05,0:01:35.49,Default,,0000,0000,0000,,here, a simple one would\Nbe something like x plus 3
Dialogue: 0,0:01:35.49,0:01:37.76,Default,,0000,0000,0000,,is equal to 10.
Dialogue: 0,0:01:37.76,0:01:40.35,Default,,0000,0000,0000,,I'm not explicitly talking\Nabout inputs and outputs
Dialogue: 0,0:01:40.35,0:01:41.77,Default,,0000,0000,0000,,or relationship\Nbetween variables.
Dialogue: 0,0:01:41.77,0:01:44.28,Default,,0000,0000,0000,,I'm just stating an equivalence.
Dialogue: 0,0:01:44.28,0:01:48.23,Default,,0000,0000,0000,,The expression x plus\N3 is equal to 10.
Dialogue: 0,0:01:48.23,0:01:50.87,Default,,0000,0000,0000,,So this, I think, traditionally\Nwould just be an equation,
Dialogue: 0,0:01:50.87,0:01:52.48,Default,,0000,0000,0000,,would not be a function.
Dialogue: 0,0:01:52.48,0:01:55.45,Default,,0000,0000,0000,,Functions essentially\Ntalk about relationships
Dialogue: 0,0:01:55.45,0:01:56.20,Default,,0000,0000,0000,,between variables.
Dialogue: 0,0:01:56.20,0:01:58.41,Default,,0000,0000,0000,,You get one or more\Ninput variables,
Dialogue: 0,0:01:58.41,0:02:01.59,Default,,0000,0000,0000,,and we'll give you only\None output variable.
Dialogue: 0,0:02:01.59,0:02:04.90,Default,,0000,0000,0000,,I'll put value.
Dialogue: 0,0:02:04.90,0:02:06.23,Default,,0000,0000,0000,,And you can define a function.
Dialogue: 0,0:02:06.23,0:02:07.44,Default,,0000,0000,0000,,And I'll do that in a second.
Dialogue: 0,0:02:07.44,0:02:09.03,Default,,0000,0000,0000,,You could define a\Nfunction as an equation,
Dialogue: 0,0:02:09.03,0:02:10.45,Default,,0000,0000,0000,,but you can define a function\Na whole bunch of ways.
Dialogue: 0,0:02:10.45,0:02:12.16,Default,,0000,0000,0000,,You can visually\Ndefine a function,
Dialogue: 0,0:02:12.16,0:02:16.79,Default,,0000,0000,0000,,maybe as a graph-- so\Nsomething like this.
Dialogue: 0,0:02:16.79,0:02:19.05,Default,,0000,0000,0000,,And maybe I actually\Nmark off the values.
Dialogue: 0,0:02:19.05,0:02:21.32,Default,,0000,0000,0000,,So that's 1, 2, 3.
Dialogue: 0,0:02:21.32,0:02:23.51,Default,,0000,0000,0000,,Those are the\Npotential x values.
Dialogue: 0,0:02:23.51,0:02:25.60,Default,,0000,0000,0000,,And then on the\Nvertical axis, I show
Dialogue: 0,0:02:25.60,0:02:27.48,Default,,0000,0000,0000,,what the value of my\Nfunction is going to be,
Dialogue: 0,0:02:27.48,0:02:29.00,Default,,0000,0000,0000,,literally my function of x.
Dialogue: 0,0:02:29.00,0:02:32.52,Default,,0000,0000,0000,,And maybe that is 1, 2, 3.
Dialogue: 0,0:02:32.52,0:02:34.20,Default,,0000,0000,0000,,And maybe this\Nfunction is defined
Dialogue: 0,0:02:34.20,0:02:36.67,Default,,0000,0000,0000,,for all non-negative values.
Dialogue: 0,0:02:36.67,0:02:38.69,Default,,0000,0000,0000,,So this is 0 of x.
Dialogue: 0,0:02:38.69,0:02:42.53,Default,,0000,0000,0000,,And so let me just draw--\Nso this right over here,
Dialogue: 0,0:02:42.53,0:02:45.01,Default,,0000,0000,0000,,at least for what I've drawn\Nso far, defines that function.
Dialogue: 0,0:02:45.01,0:02:46.68,Default,,0000,0000,0000,,I didn't even have\Nto use an equal sign.
Dialogue: 0,0:02:46.68,0:02:51.73,Default,,0000,0000,0000,,If x is 2, at least the way\NI drew it, y is equal to 3.
Dialogue: 0,0:02:51.73,0:02:52.69,Default,,0000,0000,0000,,You give me that input.
Dialogue: 0,0:02:52.69,0:02:55.88,Default,,0000,0000,0000,,I gave you the value\Nof only one output.
Dialogue: 0,0:02:55.88,0:02:57.96,Default,,0000,0000,0000,,So that would be a legitimate\Nfunction definition.
Dialogue: 0,0:02:57.96,0:02:59.34,Default,,0000,0000,0000,,Another function\Ndefinition would
Dialogue: 0,0:02:59.34,0:03:02.05,Default,,0000,0000,0000,,be very similar to what you\Ndo in a computer program,
Dialogue: 0,0:03:02.05,0:03:12.38,Default,,0000,0000,0000,,something like, let's say, that\Nyou input the day of the week.
Dialogue: 0,0:03:12.38,0:03:21.66,Default,,0000,0000,0000,,And if day is equal to Monday,\Nmaybe you output cereal.
Dialogue: 0,0:03:21.66,0:03:24.48,Default,,0000,0000,0000,,So that's what we're\Ngoing to eat that day.
Dialogue: 0,0:03:24.48,0:03:30.89,Default,,0000,0000,0000,,And otherwise, you\Noutput meatloaf.
Dialogue: 0,0:03:30.89,0:03:34.59,Default,,0000,0000,0000,,So this would also\Nbe a function.
Dialogue: 0,0:03:34.59,0:03:35.59,Default,,0000,0000,0000,,We only have one output.
Dialogue: 0,0:03:35.59,0:03:38.42,Default,,0000,0000,0000,,For any one day of\Nthe week, we can only
Dialogue: 0,0:03:38.42,0:03:40.06,Default,,0000,0000,0000,,tell you cereal or meatloaf.
Dialogue: 0,0:03:40.06,0:03:42.51,Default,,0000,0000,0000,,There's no days where you\Nare eating both cereal
Dialogue: 0,0:03:42.51,0:03:46.59,Default,,0000,0000,0000,,and meatloaf, which\Nsounds repulsive.
Dialogue: 0,0:03:46.59,0:03:49.11,Default,,0000,0000,0000,,And then if I were to\Nthink about something
Dialogue: 0,0:03:49.11,0:03:50.78,Default,,0000,0000,0000,,that could be an\Nequation or a function,
Dialogue: 0,0:03:50.78,0:03:53.30,Default,,0000,0000,0000,,I guess the way I think about\Nit is an equation is something
Dialogue: 0,0:03:53.30,0:03:55.21,Default,,0000,0000,0000,,that could be used\Nto define a function.
Dialogue: 0,0:03:55.21,0:04:03.20,Default,,0000,0000,0000,,So for example, we could say\Nthat y is equal to 4x minus 10.
Dialogue: 0,0:04:03.20,0:04:06.84,Default,,0000,0000,0000,,This is a potential\Ndefinition for defining y
Dialogue: 0,0:04:06.84,0:04:08.00,Default,,0000,0000,0000,,as a function of x.
Dialogue: 0,0:04:08.00,0:04:10.40,Default,,0000,0000,0000,,You give me any value of x.
Dialogue: 0,0:04:10.40,0:04:13.18,Default,,0000,0000,0000,,Then I can find the\Ncorresponding value of y.
Dialogue: 0,0:04:13.18,0:04:16.59,Default,,0000,0000,0000,,So this is at least how\NI would think about it.