[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.59,0:00:03.88,Default,,0000,0000,0000,,Let's do some equations that deal with absolute values.
Dialogue: 0,0:00:03.88,0:00:05.12,Default,,0000,0000,0000,,And just as a bit of a review,
Dialogue: 0,0:00:05.12,0:00:07.65,Default,,0000,0000,0000,,when you take the absolute value of a number.
Dialogue: 0,0:00:07.65,0:00:10.68,Default,,0000,0000,0000,,Let's say I take the absolute value of -1.
Dialogue: 0,0:00:10.68,0:00:12.26,Default,,0000,0000,0000,,What you're really doing is
Dialogue: 0,0:00:12.26,0:00:16.09,Default,,0000,0000,0000,,you're saying, how far is that number from 0?
Dialogue: 0,0:00:16.09,0:00:20.62,Default,,0000,0000,0000,,And in the case of -1, if we draw a number line right there
Dialogue: 0,0:00:20.62,0:00:23.31,Default,,0000,0000,0000,,-- that's a very badly\Ndrawn number line.
Dialogue: 0,0:00:23.31,0:00:26.23,Default,,0000,0000,0000,,If we draw a number line right there, that's 0.
Dialogue: 0,0:00:26.23,0:00:28.47,Default,,0000,0000,0000,,You have a -1 right there.
Dialogue: 0,0:00:28.47,0:00:30.23,Default,,0000,0000,0000,,Well, it's 1 away from 0.
Dialogue: 0,0:00:30.23,0:00:33.25,Default,,0000,0000,0000,,So the absolute value of -1 is 1.
Dialogue: 0,0:00:33.25,0:00:38.85,Default,,0000,0000,0000,,And the absolute value of 1 is also 1 away from 0.
Dialogue: 0,0:00:38.85,0:00:40.61,Default,,0000,0000,0000,,It's also equal to 1.
Dialogue: 0,0:00:40.61,0:00:43.50,Default,,0000,0000,0000,,So on some level, absolute value is the distance from 0.
Dialogue: 0,0:00:43.50,0:00:45.59,Default,,0000,0000,0000,,But another, I guess simpler way to think of it,
Dialogue: 0,0:00:45.59,0:00:48.60,Default,,0000,0000,0000,,it always results in the positive version of the number.
Dialogue: 0,0:00:48.60,0:00:59.36,Default,,0000,0000,0000,,The absolute value of -7,346 is equal to 7,346.
Dialogue: 0,0:00:59.36,0:01:00.78,Default,,0000,0000,0000,,So with that in mind, let's try to
Dialogue: 0,0:01:00.78,0:01:05.05,Default,,0000,0000,0000,,solve some equations with absolute values in them.
Dialogue: 0,0:01:05.05,0:01:06.68,Default,,0000,0000,0000,,So let's say I have the equation
Dialogue: 0,0:01:06.68,0:01:14.50,Default,,0000,0000,0000,,the absolute value of x -5 is equal to 10.
Dialogue: 0,0:01:14.50,0:01:15.90,Default,,0000,0000,0000,,And one way you can interpret this,
Dialogue: 0,0:01:15.90,0:01:18.16,Default,,0000,0000,0000,,and I want you to think about this, this is actually saying
Dialogue: 0,0:01:18.16,0:01:23.12,Default,,0000,0000,0000,,that the distance between x and 5 is equal to 10.
Dialogue: 0,0:01:23.12,0:01:26.75,Default,,0000,0000,0000,,So how many numbers that are exactly 10 away from 5?
Dialogue: 0,0:01:26.75,0:01:29.43,Default,,0000,0000,0000,,And you can already think of the solution to this equation,
Dialogue: 0,0:01:29.43,0:01:31.96,Default,,0000,0000,0000,,but I'll show you how to solve it systematically.
Dialogue: 0,0:01:31.96,0:01:36.51,Default,,0000,0000,0000,,Now this is going to be true in two situations.
Dialogue: 0,0:01:36.51,0:01:41.80,Default,,0000,0000,0000,,Either x -5 is equal to +10.
Dialogue: 0,0:01:41.80,0:01:44.63,Default,,0000,0000,0000,,If this evaluates out to +10,
Dialogue: 0,0:01:44.63,0:01:46.61,Default,,0000,0000,0000,,then when you take the absolute value of it,
Dialogue: 0,0:01:46.61,0:01:48.38,Default,,0000,0000,0000,,you're going to get +10.
Dialogue: 0,0:01:48.38,0:01:53.13,Default,,0000,0000,0000,,Or x - 5 might evaluate to -10.
Dialogue: 0,0:01:53.13,0:01:58.70,Default,,0000,0000,0000,,If x - 5 evaluated to -10, when you take the absolute value of it,
Dialogue: 0,0:01:58.70,0:01:59.95,Default,,0000,0000,0000,,you would get 10 again.
Dialogue: 0,0:01:59.95,0:02:04.28,Default,,0000,0000,0000,,So x - 5 could also be equal to -10.
Dialogue: 0,0:02:04.28,0:02:07.73,Default,,0000,0000,0000,,Both of these would satisfy this equation.
Dialogue: 0,0:02:07.73,0:02:08.96,Default,,0000,0000,0000,,Now, to solve this one,
Dialogue: 0,0:02:08.96,0:02:11.50,Default,,0000,0000,0000,,add 5 to both sides of this equation.
Dialogue: 0,0:02:11.50,0:02:14.16,Default,,0000,0000,0000,,You get x is equal to 15.
Dialogue: 0,0:02:14.16,0:02:17.83,Default,,0000,0000,0000,,To solve this one, add 5 to both sides of this equation.
Dialogue: 0,0:02:17.83,0:02:20.90,Default,,0000,0000,0000,,x is equal to -5.
Dialogue: 0,0:02:20.90,0:02:21.96,Default,,0000,0000,0000,,So our solution,
Dialogue: 0,0:02:21.96,0:02:24.91,Default,,0000,0000,0000,,there's two x's that satisfy this equation.
Dialogue: 0,0:02:24.91,0:02:26.89,Default,,0000,0000,0000,,x could be 15.
Dialogue: 0,0:02:26.89,0:02:29.50,Default,,0000,0000,0000,,15 - 5 is 10, take the absolute value,
Dialogue: 0,0:02:29.50,0:02:32.69,Default,,0000,0000,0000,,you're going to get 10, or x could be -5.
Dialogue: 0,0:02:32.69,0:02:36.06,Default,,0000,0000,0000,,- 5 minus 5 is -10.
Dialogue: 0,0:02:36.06,0:02:39.02,Default,,0000,0000,0000,,Take the absolute value, you get 10.
Dialogue: 0,0:02:39.02,0:02:41.63,Default,,0000,0000,0000,,And notice, both of these numbers
Dialogue: 0,0:02:41.63,0:02:45.75,Default,,0000,0000,0000,,are exactly 10 away from the number 5.
Dialogue: 0,0:02:45.75,0:02:48.05,Default,,0000,0000,0000,,Let's do another one of these.
Dialogue: 0,0:02:48.05,0:02:51.13,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:02:51.13,0:02:52.18,Default,,0000,0000,0000,,Let's say we have
Dialogue: 0,0:02:52.18,0:02:58.58,Default,,0000,0000,0000,,the absolute value of x + 2 is equal to 6.
Dialogue: 0,0:02:58.58,0:02:59.61,Default,,0000,0000,0000,,So what does that tell us?
Dialogue: 0,0:02:59.61,0:03:03.13,Default,,0000,0000,0000,,That tells us that either x + 2,
Dialogue: 0,0:03:03.13,0:03:07.03,Default,,0000,0000,0000,,that the thing inside the absolute value sign, is equal to 6.
Dialogue: 0,0:03:07.03,0:03:10.38,Default,,0000,0000,0000,,Or the thing inside of the absolute value sign,
Dialogue: 0,0:03:10.38,0:03:12.05,Default,,0000,0000,0000,,the x + 2, could also be -6.
Dialogue: 0,0:03:12.05,0:03:13.91,Default,,0000,0000,0000,,If this whole thing evaluated to -6,
Dialogue: 0,0:03:13.91,0:03:16.21,Default,,0000,0000,0000,,you take the absolute value, you'd get 6.
Dialogue: 0,0:03:16.21,0:03:20.34,Default,,0000,0000,0000,,So, or x + 2 could equal -6.
Dialogue: 0,0:03:20.34,0:03:22.88,Default,,0000,0000,0000,,And then if you subtract 2 from both sides of this equation,
Dialogue: 0,0:03:22.88,0:03:25.85,Default,,0000,0000,0000,,you get x could be equal to 4.
Dialogue: 0,0:03:25.85,0:03:29.78,Default,,0000,0000,0000,,If you subtract 2 from both sides of this equation,
Dialogue: 0,0:03:29.78,0:03:33.69,Default,,0000,0000,0000,,you get x could be equal to -8.
Dialogue: 0,0:03:33.69,0:03:37.24,Default,,0000,0000,0000,,So these are the two solutions to the equation.
Dialogue: 0,0:03:37.24,0:03:39.74,Default,,0000,0000,0000,,And just to kind of have it gel in your mind,
Dialogue: 0,0:03:39.74,0:03:42.50,Default,,0000,0000,0000,,that absolute value, you can kind of view it as a distance,
Dialogue: 0,0:03:42.50,0:03:43.94,Default,,0000,0000,0000,,you could rewrite this problem
Dialogue: 0,0:03:43.94,0:03:50.41,Default,,0000,0000,0000,,as the absolute value of x minus -2 is equal to 6.
Dialogue: 0,0:03:50.41,0:03:52.76,Default,,0000,0000,0000,,And so this is asking me,
Dialogue: 0,0:03:52.76,0:03:57.59,Default,,0000,0000,0000,,what are the x's that are exactly 6 away from -2?
Dialogue: 0,0:03:57.59,0:03:59.17,Default,,0000,0000,0000,,Remember, up here we said,
Dialogue: 0,0:03:59.17,0:04:03.56,Default,,0000,0000,0000,,what are the x's that are exactly 10 away from +5?
Dialogue: 0,0:04:03.56,0:04:05.99,Default,,0000,0000,0000,,Whatever number you're subtracting from +5,
Dialogue: 0,0:04:05.99,0:04:08.56,Default,,0000,0000,0000,,these are both 10 away from +5.
Dialogue: 0,0:04:08.56,0:04:09.52,Default,,0000,0000,0000,,This is asking,
Dialogue: 0,0:04:09.52,0:04:13.08,Default,,0000,0000,0000,,what is exactly 6 away from -2?
Dialogue: 0,0:04:13.08,0:04:15.51,Default,,0000,0000,0000,,And it's going to be 4, or -8.
Dialogue: 0,0:04:15.51,0:04:17.96,Default,,0000,0000,0000,,You could try those numbers out for yourself.
Dialogue: 0,0:04:17.96,0:04:20.46,Default,,0000,0000,0000,,Let's do another one of these.
Dialogue: 0,0:04:20.46,0:04:25.33,Default,,0000,0000,0000,,Let's do another one, and we'll do it in purple.
Dialogue: 0,0:04:25.33,0:04:30.19,Default,,0000,0000,0000,,Let's say we have the absolute value of 4x.
Dialogue: 0,0:04:30.19,0:04:31.43,Default,,0000,0000,0000,,I'm going to change this problem up a little bit.
Dialogue: 0,0:04:31.43,0:04:33.39,Default,,0000,0000,0000,,4x -1.
Dialogue: 0,0:04:33.39,0:04:36.58,Default,,0000,0000,0000,,The absolute value of 4x -1, is equal to--
Dialogue: 0,0:04:36.58,0:04:40.20,Default,,0000,0000,0000,,actually, I'll just keep it-- is equal to 19.
Dialogue: 0,0:04:40.20,0:04:41.77,Default,,0000,0000,0000,,So, just like the last few problems,
Dialogue: 0,0:04:41.77,0:04:47.64,Default,,0000,0000,0000,,4x -1 could be equal to 19.
Dialogue: 0,0:04:47.64,0:04:51.67,Default,,0000,0000,0000,,Or 4x -1 might evaluate to -19.
Dialogue: 0,0:04:51.67,0:04:53.13,Default,,0000,0000,0000,,Because then when you take the absolute value,
Dialogue: 0,0:04:53.13,0:04:54.80,Default,,0000,0000,0000,,you're going to get 19 again.
Dialogue: 0,0:04:54.80,0:04:59.10,Default,,0000,0000,0000,,Or 4x -1 could be equal to -19.
Dialogue: 0,0:04:59.10,0:05:00.97,Default,,0000,0000,0000,,Then you just solve these two equations.
Dialogue: 0,0:05:00.97,0:05:02.94,Default,,0000,0000,0000,,Add 1 to both sides of this equation--
Dialogue: 0,0:05:02.94,0:05:04.27,Default,,0000,0000,0000,,we could do them simultaneous, even.
Dialogue: 0,0:05:04.27,0:05:08.51,Default,,0000,0000,0000,,Add 1 to both sides of this, you get 4x is equal to 20.
Dialogue: 0,0:05:08.51,0:05:11.00,Default,,0000,0000,0000,,Add 1 to both sides of this equation,
Dialogue: 0,0:05:11.00,0:05:15.34,Default,,0000,0000,0000,,you get 4x is equal to -18.
Dialogue: 0,0:05:15.34,0:05:20.21,Default,,0000,0000,0000,,Divide both sides of this by 4, you get x is equal to 5.
Dialogue: 0,0:05:20.21,0:05:23.92,Default,,0000,0000,0000,,Divide both sides of this by 4, you get x is equal to -18/4,
Dialogue: 0,0:05:23.92,0:05:31.77,Default,,0000,0000,0000,,which is equal to -9/2.
Dialogue: 0,0:05:31.77,0:05:35.73,Default,,0000,0000,0000,,So both of these x values satisfy the equation.
Dialogue: 0,0:05:35.73,0:05:36.59,Default,,0000,0000,0000,,Try it out.
Dialogue: 0,0:05:36.59,0:05:39.58,Default,,0000,0000,0000,,-9/2 x 4.
Dialogue: 0,0:05:39.58,0:05:41.57,Default,,0000,0000,0000,,This will become a -18.
Dialogue: 0,0:05:41.57,0:05:44.20,Default,,0000,0000,0000,,-18 minus 1 is -19.
Dialogue: 0,0:05:44.20,0:05:46.74,Default,,0000,0000,0000,,Take the absolute value, you get 19.
Dialogue: 0,0:05:46.74,0:05:49.92,Default,,0000,0000,0000,,You put a 5 here, 4 x 5 is 20.
Dialogue: 0,0:05:49.92,0:05:51.96,Default,,0000,0000,0000,,Minus 1 is +19.
Dialogue: 0,0:05:51.96,0:05:53.26,Default,,0000,0000,0000,,So you take the absolute value.
Dialogue: 0,0:05:53.26,0:05:55.92,Default,,0000,0000,0000,,Once again, you'll get a 19.
Dialogue: 0,0:05:55.92,0:05:58.58,Default,,0000,0000,0000,,Let's try to graph one of these, just for fun.
Dialogue: 0,0:05:58.58,0:05:59.28,Default,,0000,0000,0000,,So let's say
Dialogue: 0,0:05:59.28,0:06:04.99,Default,,0000,0000,0000,,I have y is equal to the absolute value of x +3.
Dialogue: 0,0:06:04.99,0:06:07.84,Default,,0000,0000,0000,,So this is a function, or a graph,
Dialogue: 0,0:06:07.84,0:06:09.41,Default,,0000,0000,0000,,with an absolute value in it.
Dialogue: 0,0:06:09.41,0:06:11.82,Default,,0000,0000,0000,,So let's think about two scenarios.
Dialogue: 0,0:06:11.82,0:06:13.14,Default,,0000,0000,0000,,There's one scenario
Dialogue: 0,0:06:13.14,0:06:16.43,Default,,0000,0000,0000,,where the thing inside of the absolute value is positive.
Dialogue: 0,0:06:16.43,0:06:18.87,Default,,0000,0000,0000,,So you have the scenario where x + 3
Dialogue: 0,0:06:18.87,0:06:23.42,Default,,0000,0000,0000,,I'll write it over here: x + 3 is > 0.
Dialogue: 0,0:06:23.42,0:06:29.37,Default,,0000,0000,0000,,And then you have the scenario where x +3 is < 0.
Dialogue: 0,0:06:29.37,0:06:32.66,Default,,0000,0000,0000,,When x +3 is > 0,\N
Dialogue: 0,0:06:32.66,0:06:36.49,Default,,0000,0000,0000,,this graph, or this line--or I guess we can't call it a line--
Dialogue: 0,0:06:36.49,0:06:41.69,Default,,0000,0000,0000,,this function, is the same thing as y is equal to x +3.
Dialogue: 0,0:06:41.69,0:06:44.37,Default,,0000,0000,0000,,If this thing over here is > 0,
Dialogue: 0,0:06:44.37,0:06:46.75,Default,,0000,0000,0000,,then the absolute value sign is irrelevant.
Dialogue: 0,0:06:46.75,0:06:48.78,Default,,0000,0000,0000,,So then this thing is the same thing
Dialogue: 0,0:06:48.78,0:06:50.28,Default,,0000,0000,0000,,as y is equal to x +3.
Dialogue: 0,0:06:50.28,0:06:52.59,Default,,0000,0000,0000,,But when is x +3 > 0?
Dialogue: 0,0:06:52.59,0:06:56.37,Default,,0000,0000,0000,,Well, if you subtract 3 from both sides,
Dialogue: 0,0:06:56.37,0:06:59.91,Default,,0000,0000,0000,,you get x is > -3.
Dialogue: 0,0:06:59.91,0:07:02.25,Default,,0000,0000,0000,,So when x is > -3,
Dialogue: 0,0:07:02.25,0:07:08.46,Default,,0000,0000,0000,,this graph is going to look just like y is equal to x +3.
Dialogue: 0,0:07:08.46,0:07:11.50,Default,,0000,0000,0000,,Now, when x +3 is < 0.
Dialogue: 0,0:07:11.50,0:07:13.33,Default,,0000,0000,0000,,When the situation where this--
Dialogue: 0,0:07:13.33,0:07:16.51,Default,,0000,0000,0000,,the inside of our absolute value sign--is negative,
Dialogue: 0,0:07:16.51,0:07:20.36,Default,,0000,0000,0000,,in that situation this equation is going to be
Dialogue: 0,0:07:20.36,0:07:26.25,Default,,0000,0000,0000,,y is equal to the negative of x +3.
Dialogue: 0,0:07:26.25,0:07:27.54,Default,,0000,0000,0000,,How can I say that?
Dialogue: 0,0:07:27.54,0:07:30.52,Default,,0000,0000,0000,,Well, look, if this is going to\Nbe a negative number, if x
Dialogue: 0,0:07:30.52,0:07:33.06,Default,,0000,0000,0000,,plus 3 is going to be a negative\Nnumber-- that's what
Dialogue: 0,0:07:33.06,0:07:36.01,Default,,0000,0000,0000,,we're assuming here-- if it's\Ngoing to be a negative number,
Dialogue: 0,0:07:36.01,0:07:38.09,Default,,0000,0000,0000,,then when you take the absolute\Nvalue of a negative
Dialogue: 0,0:07:38.09,0:07:40.05,Default,,0000,0000,0000,,number, you're going to\Nmake it positive.
Dialogue: 0,0:07:40.05,0:07:43.28,Default,,0000,0000,0000,,That's just like multiplying\Nit by negative 1.
Dialogue: 0,0:07:43.28,0:07:45.87,Default,,0000,0000,0000,,If you know you're taking the\Nabsolute value of a negative
Dialogue: 0,0:07:45.87,0:07:48.89,Default,,0000,0000,0000,,number, it's just like\Nmultiplying it by negative 1,
Dialogue: 0,0:07:48.89,0:07:51.01,Default,,0000,0000,0000,,because you're going to\Nmake it positive.
Dialogue: 0,0:07:51.01,0:07:53.87,Default,,0000,0000,0000,,And this is going to\Nbe the situation.
Dialogue: 0,0:07:53.87,0:07:55.84,Default,,0000,0000,0000,,x plus 3 is less than 0.
Dialogue: 0,0:07:55.84,0:07:59.85,Default,,0000,0000,0000,,If we subtract 3 from both\Nsides, when x is less than
Dialogue: 0,0:07:59.85,0:08:01.28,Default,,0000,0000,0000,,negative 3.
Dialogue: 0,0:08:01.28,0:08:03.92,Default,,0000,0000,0000,,So when x is less than negative\N3, the graph will
Dialogue: 0,0:08:03.92,0:08:05.04,Default,,0000,0000,0000,,look like this.
Dialogue: 0,0:08:05.04,0:08:08.28,Default,,0000,0000,0000,,When x is greater than negative\N3, the graph will
Dialogue: 0,0:08:08.28,0:08:09.60,Default,,0000,0000,0000,,look like that.
Dialogue: 0,0:08:09.60,0:08:11.30,Default,,0000,0000,0000,,So let's see what that\Nwould make the
Dialogue: 0,0:08:11.30,0:08:13.67,Default,,0000,0000,0000,,entire graph look like.
Dialogue: 0,0:08:13.67,0:08:21.52,Default,,0000,0000,0000,,Let me draw my axes.
Dialogue: 0,0:08:21.52,0:08:26.07,Default,,0000,0000,0000,,That's my x-axis, that's\Nmy y-axis.
Dialogue: 0,0:08:26.07,0:08:29.09,Default,,0000,0000,0000,,So just let me multiply this\Nout, just so we have it in mx
Dialogue: 0,0:08:29.09,0:08:29.87,Default,,0000,0000,0000,,plus b form.
Dialogue: 0,0:08:29.87,0:08:36.07,Default,,0000,0000,0000,,So this is equal to negative\Nx minus 3.
Dialogue: 0,0:08:36.07,0:08:37.41,Default,,0000,0000,0000,,So let's just figure out\Nwhat this graph would
Dialogue: 0,0:08:37.41,0:08:38.62,Default,,0000,0000,0000,,look like in general.
Dialogue: 0,0:08:38.62,0:08:42.02,Default,,0000,0000,0000,,Negative x minus 3.
Dialogue: 0,0:08:42.02,0:08:47.38,Default,,0000,0000,0000,,The y-intercept is negative\N3, so 1, 2, 3.
Dialogue: 0,0:08:47.38,0:08:51.06,Default,,0000,0000,0000,,And negative x means it\Nslopes downward, has a
Dialogue: 0,0:08:51.06,0:08:52.29,Default,,0000,0000,0000,,downward slope of 1.
Dialogue: 0,0:08:52.29,0:08:53.54,Default,,0000,0000,0000,,So it would look like this.
Dialogue: 0,0:08:56.84,0:09:02.83,Default,,0000,0000,0000,,The x-intercept would be\Nat x is equal to--.
Dialogue: 0,0:09:02.83,0:09:07.74,Default,,0000,0000,0000,,So if you say y is equal to 0,\Nthat would happen when x is
Dialogue: 0,0:09:07.74,0:09:08.58,Default,,0000,0000,0000,,equal to negative 3.
Dialogue: 0,0:09:08.58,0:09:10.38,Default,,0000,0000,0000,,So it's going to go\Nthrough that line,
Dialogue: 0,0:09:10.38,0:09:11.92,Default,,0000,0000,0000,,that point right there.
Dialogue: 0,0:09:11.92,0:09:14.19,Default,,0000,0000,0000,,And the graph, if we didn't\Nhave this constraint right
Dialogue: 0,0:09:14.19,0:09:15.60,Default,,0000,0000,0000,,here, would look something\Nlike this.
Dialogue: 0,0:09:19.89,0:09:22.76,Default,,0000,0000,0000,,That's if we didn't constrain\Nit to a certain interval on
Dialogue: 0,0:09:22.76,0:09:23.88,Default,,0000,0000,0000,,the x-axis.
Dialogue: 0,0:09:23.88,0:09:27.08,Default,,0000,0000,0000,,Now this graph, what\Ndoes it look like?
Dialogue: 0,0:09:27.08,0:09:27.48,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:09:27.48,0:09:31.81,Default,,0000,0000,0000,,It has its y-intercept\Nat positive 3.
Dialogue: 0,0:09:31.81,0:09:33.23,Default,,0000,0000,0000,,Just like that.
Dialogue: 0,0:09:33.23,0:09:35.26,Default,,0000,0000,0000,,And where's its x-intecept?
Dialogue: 0,0:09:35.26,0:09:37.97,Default,,0000,0000,0000,,When y is equal to 0,\Nx is negative 3.
Dialogue: 0,0:09:37.97,0:09:39.76,Default,,0000,0000,0000,,So it also goes through that\Npoint right there, and it has
Dialogue: 0,0:09:39.76,0:09:40.62,Default,,0000,0000,0000,,a slope of 1.
Dialogue: 0,0:09:40.62,0:09:43.71,Default,,0000,0000,0000,,So it would look something\Nlike this.
Dialogue: 0,0:09:43.71,0:09:45.33,Default,,0000,0000,0000,,That's what this graph\Nlooks like.
Dialogue: 0,0:09:45.33,0:09:48.10,Default,,0000,0000,0000,,Now, what we figured out is\Nthat this absolute value
Dialogue: 0,0:09:48.10,0:09:52.03,Default,,0000,0000,0000,,function, it looks like this\Npurple graph when x is less
Dialogue: 0,0:09:52.03,0:09:53.83,Default,,0000,0000,0000,,than negative 3.
Dialogue: 0,0:09:53.83,0:09:57.07,Default,,0000,0000,0000,,So when x is less than negative\N3-- that's x is equal
Dialogue: 0,0:09:57.07,0:09:59.59,Default,,0000,0000,0000,,to negative 3 right there-- when\Nx is less than negative
Dialogue: 0,0:09:59.59,0:10:03.17,Default,,0000,0000,0000,,3, it looks like this\Npurple graph.
Dialogue: 0,0:10:03.17,0:10:04.57,Default,,0000,0000,0000,,Right there.
Dialogue: 0,0:10:04.57,0:10:07.39,Default,,0000,0000,0000,,So that's when x is less\Nthan negative 3.
Dialogue: 0,0:10:07.39,0:10:10.83,Default,,0000,0000,0000,,But when x is greater than\Nnegative 3, it looks like the
Dialogue: 0,0:10:10.83,0:10:12.16,Default,,0000,0000,0000,,green graph.
Dialogue: 0,0:10:12.16,0:10:14.64,Default,,0000,0000,0000,,It looks like that.
Dialogue: 0,0:10:14.64,0:10:17.48,Default,,0000,0000,0000,,So this graph looks like\Nthis strange v.
Dialogue: 0,0:10:17.48,0:10:21.43,Default,,0000,0000,0000,,When x is greater than negative\N3, this is positive.
Dialogue: 0,0:10:21.43,0:10:24.95,Default,,0000,0000,0000,,So we have the graph of-- we\Nhave a positive slope.
Dialogue: 0,0:10:24.95,0:10:28.27,Default,,0000,0000,0000,,But then when x is less than\Nnegative 3, we're essentially
Dialogue: 0,0:10:28.27,0:10:30.55,Default,,0000,0000,0000,,taking the negative of the\Nfunction, if you want to view
Dialogue: 0,0:10:30.55,0:10:32.28,Default,,0000,0000,0000,,it that way, and so we have\Nthis negative slope.
Dialogue: 0,0:10:32.28,0:10:35.06,Default,,0000,0000,0000,,So you kind of have this\Nv-shaped function, this
Dialogue: 0,0:10:35.06,0:10:38.25,Default,,0000,0000,0000,,v-shaped graph, which is\Nindicative of an absolute
Dialogue: 0,0:10:38.25,0:10:39.95,Default,,0000,0000,0000,,value function.