[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.59,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.59,0:00:05.69,Default,,0000,0000,0000,,We're asked to graph, y is\Nequal to log base 5 of x.
Dialogue: 0,0:00:05.69,0:00:07.78,Default,,0000,0000,0000,,And just to remind us\Nwhat this is saying,
Dialogue: 0,0:00:07.78,0:00:10.24,Default,,0000,0000,0000,,this is saying that y\Nis equal to the power
Dialogue: 0,0:00:10.24,0:00:13.46,Default,,0000,0000,0000,,that I have to raise\N5 to to get to x.
Dialogue: 0,0:00:13.46,0:00:15.98,Default,,0000,0000,0000,,Or if I were to write\Nthis logarithmic equation
Dialogue: 0,0:00:15.98,0:00:19.51,Default,,0000,0000,0000,,as an exponential\Nequation, 5 is my base,
Dialogue: 0,0:00:19.51,0:00:23.64,Default,,0000,0000,0000,,y is the exponent that I\Nhave to raise my base to,
Dialogue: 0,0:00:23.64,0:00:28.42,Default,,0000,0000,0000,,and then x is what I get when\NI raise 5 to the yth power.
Dialogue: 0,0:00:28.42,0:00:32.57,Default,,0000,0000,0000,,So another way of writing\Nthis equation would be 5
Dialogue: 0,0:00:32.57,0:00:40.71,Default,,0000,0000,0000,,to the y'th power is\Ngoing to be equal to x.
Dialogue: 0,0:00:40.71,0:00:43.01,Default,,0000,0000,0000,,These are the same thing.
Dialogue: 0,0:00:43.01,0:00:45.48,Default,,0000,0000,0000,,Here, we have y as\Na function of x.
Dialogue: 0,0:00:45.48,0:00:48.55,Default,,0000,0000,0000,,Here, we have x as\Na function of y.
Dialogue: 0,0:00:48.55,0:00:50.98,Default,,0000,0000,0000,,But they're really saying\Nthe exact same thing,
Dialogue: 0,0:00:50.98,0:00:53.62,Default,,0000,0000,0000,,raise 5 to the y'th\Npower to get x.
Dialogue: 0,0:00:53.62,0:00:55.79,Default,,0000,0000,0000,,When you put it as a\Nlogarithm, you're saying, well,
Dialogue: 0,0:00:55.79,0:00:58.01,Default,,0000,0000,0000,,what power do I have\Nto raise 5 to to get x?
Dialogue: 0,0:00:58.01,0:00:59.44,Default,,0000,0000,0000,,We'll have to raise it to y.
Dialogue: 0,0:00:59.44,0:01:02.94,Default,,0000,0000,0000,,Here, what do I get when I\Nraise five to the y power?
Dialogue: 0,0:01:02.94,0:01:04.10,Default,,0000,0000,0000,,I get x.
Dialogue: 0,0:01:04.10,0:01:07.20,Default,,0000,0000,0000,,That out of the way, let's\Nmake ourselves a little table
Dialogue: 0,0:01:07.20,0:01:08.71,Default,,0000,0000,0000,,that we can use to\Nplot some points,
Dialogue: 0,0:01:08.71,0:01:10.34,Default,,0000,0000,0000,,and then we can\Nconnect the dots to see
Dialogue: 0,0:01:10.34,0:01:11.98,Default,,0000,0000,0000,,what this curve looks like.
Dialogue: 0,0:01:11.98,0:01:13.94,Default,,0000,0000,0000,,So let me pick some\Nx's and some y's.
Dialogue: 0,0:01:13.94,0:01:18.50,Default,,0000,0000,0000,,
Dialogue: 0,0:01:18.50,0:01:21.10,Default,,0000,0000,0000,,And we, in general, want to\Npick some numbers that give us
Dialogue: 0,0:01:21.10,0:01:24.69,Default,,0000,0000,0000,,some nice round answers, some\Nnice fairly simple numbers
Dialogue: 0,0:01:24.69,0:01:26.23,Default,,0000,0000,0000,,for us to deal with,\Nso that we don't
Dialogue: 0,0:01:26.23,0:01:27.76,Default,,0000,0000,0000,,have to get the calculator.
Dialogue: 0,0:01:27.76,0:01:29.59,Default,,0000,0000,0000,,And so in general,\Nyou want to pick
Dialogue: 0,0:01:29.59,0:01:34.25,Default,,0000,0000,0000,,x values where the power\Nthat you have to raise 5
Dialogue: 0,0:01:34.25,0:01:38.16,Default,,0000,0000,0000,,to to get that x value is a\Npretty straightforward power.
Dialogue: 0,0:01:38.16,0:01:39.53,Default,,0000,0000,0000,,Or another way to\Nthink about it,
Dialogue: 0,0:01:39.53,0:01:41.81,Default,,0000,0000,0000,,you could just think about\Nthe different y values
Dialogue: 0,0:01:41.81,0:01:44.74,Default,,0000,0000,0000,,that you want to raise\N5 to the power of,
Dialogue: 0,0:01:44.74,0:01:46.36,Default,,0000,0000,0000,,and then you could\Nget your x values.
Dialogue: 0,0:01:46.36,0:01:48.59,Default,,0000,0000,0000,,So we could actually\Nthink about this one
Dialogue: 0,0:01:48.59,0:01:52.51,Default,,0000,0000,0000,,to come up with our\Nactual x values.
Dialogue: 0,0:01:52.51,0:01:56.37,Default,,0000,0000,0000,,But we want to be clear that\Nwhen we express it like this,
Dialogue: 0,0:01:56.37,0:01:59.85,Default,,0000,0000,0000,,the independent variable is x,\Nand the dependent variable is
Dialogue: 0,0:01:59.85,0:02:00.48,Default,,0000,0000,0000,,y.
Dialogue: 0,0:02:00.48,0:02:03.66,Default,,0000,0000,0000,,We might just look at\Nthis one to pick some nice
Dialogue: 0,0:02:03.66,0:02:10.44,Default,,0000,0000,0000,,even or nice x's that give\Nus nice clean answers for y.
Dialogue: 0,0:02:10.44,0:02:12.69,Default,,0000,0000,0000,,So here, I'm actually going\Nto fill in the y first,
Dialogue: 0,0:02:12.69,0:02:14.82,Default,,0000,0000,0000,,just so we get nice clean x's.
Dialogue: 0,0:02:14.82,0:02:16.50,Default,,0000,0000,0000,,So let's say we're\Ngoing to raise five
Dialogue: 0,0:02:16.50,0:02:19.12,Default,,0000,0000,0000,,to the-- let's say we're going\Nto raise it-- I'm going to pick
Dialogue: 0,0:02:19.12,0:02:23.82,Default,,0000,0000,0000,,some new colors-- negative\N2, negative 2 power--
Dialogue: 0,0:02:23.82,0:02:30.49,Default,,0000,0000,0000,,and let me do some other\Ncolors-- negative 1, 0, 1.
Dialogue: 0,0:02:30.49,0:02:33.62,Default,,0000,0000,0000,,I'll do one more, and then 2.
Dialogue: 0,0:02:33.62,0:02:36.66,Default,,0000,0000,0000,,So once again, this is\Na little nontraditional,
Dialogue: 0,0:02:36.66,0:02:38.89,Default,,0000,0000,0000,,where I'm filling in the\Ndependent variable first.
Dialogue: 0,0:02:38.89,0:02:40.30,Default,,0000,0000,0000,,But the way that\Nwe've written it over
Dialogue: 0,0:02:40.30,0:02:42.29,Default,,0000,0000,0000,,here, it's actually given\Nthe dependent variable,
Dialogue: 0,0:02:42.29,0:02:44.75,Default,,0000,0000,0000,,it's easy to figure out what\Nthe independent variable needs
Dialogue: 0,0:02:44.75,0:02:47.13,Default,,0000,0000,0000,,to be for this\Nlogarithmic function.
Dialogue: 0,0:02:47.13,0:02:50.42,Default,,0000,0000,0000,,So, what x gives me\Na y of negative 2?
Dialogue: 0,0:02:50.42,0:02:52.64,Default,,0000,0000,0000,,What x gives me--\Nwhat does x have
Dialogue: 0,0:02:52.64,0:02:55.43,Default,,0000,0000,0000,,to be for y to be\Nequal to negative 2?
Dialogue: 0,0:02:55.43,0:02:59.59,Default,,0000,0000,0000,,Well, 5 to the negative 2 power\Nis going to be equal to x.
Dialogue: 0,0:02:59.59,0:03:04.48,Default,,0000,0000,0000,,So 5 to the negative\N2 is 1 over 25.
Dialogue: 0,0:03:04.48,0:03:07.44,Default,,0000,0000,0000,,So we get 1 over 25.
Dialogue: 0,0:03:07.44,0:03:09.00,Default,,0000,0000,0000,,If we go back to\Nthis earlier one,
Dialogue: 0,0:03:09.00,0:03:13.20,Default,,0000,0000,0000,,if we say log base\N5 of 1 over 25,
Dialogue: 0,0:03:13.20,0:03:16.53,Default,,0000,0000,0000,,what power do I have to\Nraise 5 to to get 1 over 25?
Dialogue: 0,0:03:16.53,0:03:19.42,Default,,0000,0000,0000,,We'll have to raise it\Nto the negative 2 power.
Dialogue: 0,0:03:19.42,0:03:22.11,Default,,0000,0000,0000,,Or you could say 5\Nto the negative 2
Dialogue: 0,0:03:22.11,0:03:24.46,Default,,0000,0000,0000,,is equal to 1 over 25.
Dialogue: 0,0:03:24.46,0:03:27.96,Default,,0000,0000,0000,,These are saying the\Nexact same thing.
Dialogue: 0,0:03:27.96,0:03:30.16,Default,,0000,0000,0000,,Now let's do another one.
Dialogue: 0,0:03:30.16,0:03:34.10,Default,,0000,0000,0000,,What happens when I raise\N5 to the negative 1 power?
Dialogue: 0,0:03:34.10,0:03:35.49,Default,,0000,0000,0000,,I get one fifth.
Dialogue: 0,0:03:35.49,0:03:37.32,Default,,0000,0000,0000,,So if we go to this\Noriginal one over there,
Dialogue: 0,0:03:37.32,0:03:42.67,Default,,0000,0000,0000,,we're just saying that\Nlog base 5 of one fifth.
Dialogue: 0,0:03:42.67,0:03:44.21,Default,,0000,0000,0000,,Want to be careful.
Dialogue: 0,0:03:44.21,0:03:46.81,Default,,0000,0000,0000,,This is saying, what power\Ndo I have to raise 5 to
Dialogue: 0,0:03:46.81,0:03:48.13,Default,,0000,0000,0000,,in order to get one fifth.
Dialogue: 0,0:03:48.13,0:03:50.64,Default,,0000,0000,0000,,We'll have to raise it\Nto the negative 1 power.
Dialogue: 0,0:03:50.64,0:03:53.15,Default,,0000,0000,0000,,
Dialogue: 0,0:03:53.15,0:03:55.08,Default,,0000,0000,0000,,What happens when I take\N5 to the 0'th power?
Dialogue: 0,0:03:55.08,0:03:57.25,Default,,0000,0000,0000,,I get one.
Dialogue: 0,0:03:57.25,0:03:59.29,Default,,0000,0000,0000,,And so this relationship--\NThis is the same thing
Dialogue: 0,0:03:59.29,0:04:02.65,Default,,0000,0000,0000,,as saying log base 5 of 1.
Dialogue: 0,0:04:02.65,0:04:05.43,Default,,0000,0000,0000,,What power do I have\Nto raise 5 to to get 1?
Dialogue: 0,0:04:05.43,0:04:08.91,Default,,0000,0000,0000,,I just have to raise\Nit to the 0th power.
Dialogue: 0,0:04:08.91,0:04:10.66,Default,,0000,0000,0000,,Let's do the next two.
Dialogue: 0,0:04:10.66,0:04:13.47,Default,,0000,0000,0000,,What happens when I raise\N5 to the first power?
Dialogue: 0,0:04:13.47,0:04:17.18,Default,,0000,0000,0000,,Well, I get 5 So if you go look\Nover here, that's just saying,
Dialogue: 0,0:04:17.18,0:04:20.41,Default,,0000,0000,0000,,log, what power do I have\Nto raise 5 to to get 5?
Dialogue: 0,0:04:20.41,0:04:23.88,Default,,0000,0000,0000,,We'll have to just raise\Nit to the first power.
Dialogue: 0,0:04:23.88,0:04:28.80,Default,,0000,0000,0000,,And then finally, if I\Ntake 5 squared, I get 25.
Dialogue: 0,0:04:28.80,0:04:31.68,Default,,0000,0000,0000,,So when you look at it from\Nthe logarithmic point of view,
Dialogue: 0,0:04:31.68,0:04:34.41,Default,,0000,0000,0000,,you say, well, what power\Ndo I have to raise 5 to
Dialogue: 0,0:04:34.41,0:04:36.02,Default,,0000,0000,0000,,to get to 25?
Dialogue: 0,0:04:36.02,0:04:38.93,Default,,0000,0000,0000,,We'll have to raise it\Nto the second power.
Dialogue: 0,0:04:38.93,0:04:41.83,Default,,0000,0000,0000,,So I took the inverse of\Nthe logarithmic function.
Dialogue: 0,0:04:41.83,0:04:43.55,Default,,0000,0000,0000,,I wrote it as an\Nexponential function.
Dialogue: 0,0:04:43.55,0:04:47.27,Default,,0000,0000,0000,,I switched the dependent\Nand independent variables,
Dialogue: 0,0:04:47.27,0:04:50.76,Default,,0000,0000,0000,,so I can derive nice clean x's\Nthat will give me nice clean
Dialogue: 0,0:04:50.76,0:04:51.73,Default,,0000,0000,0000,,y's.
Dialogue: 0,0:04:51.73,0:04:54.15,Default,,0000,0000,0000,,Now with that out of the way,\Nbut I do want to remind you,
Dialogue: 0,0:04:54.15,0:04:57.50,Default,,0000,0000,0000,,I could have just picked\Nrandom numbers over here,
Dialogue: 0,0:04:57.50,0:04:59.83,Default,,0000,0000,0000,,but then I would have probably\Ngotten less clean numbers
Dialogue: 0,0:04:59.83,0:05:00.26,Default,,0000,0000,0000,,over here.
Dialogue: 0,0:05:00.26,0:05:01.51,Default,,0000,0000,0000,,I would have had to\Nuse a calculator.
Dialogue: 0,0:05:01.51,0:05:03.09,Default,,0000,0000,0000,,The only reason why\NI did it this way,
Dialogue: 0,0:05:03.09,0:05:06.81,Default,,0000,0000,0000,,is so I get nice clean results\Nthat I can plot by hand.
Dialogue: 0,0:05:06.81,0:05:08.74,Default,,0000,0000,0000,,So let's actually graph it.
Dialogue: 0,0:05:08.74,0:05:10.91,Default,,0000,0000,0000,,Let's actually graph\Nthis thing over here.
Dialogue: 0,0:05:10.91,0:05:13.57,Default,,0000,0000,0000,,So the y's go between\Nnegative 2 and 2.
Dialogue: 0,0:05:13.57,0:05:18.65,Default,,0000,0000,0000,,The x's go from 1/25th\Nall the way to 25.
Dialogue: 0,0:05:18.65,0:05:22.68,Default,,0000,0000,0000,,So let's graph it.
Dialogue: 0,0:05:22.68,0:05:30.05,Default,,0000,0000,0000,,So that is my y-axis,\Nand this is my x-axis.
Dialogue: 0,0:05:30.05,0:05:32.12,Default,,0000,0000,0000,,Draw it like that.
Dialogue: 0,0:05:32.12,0:05:34.19,Default,,0000,0000,0000,,That is my x-axis.
Dialogue: 0,0:05:34.19,0:05:37.34,Default,,0000,0000,0000,,And then the y's start at 0.
Dialogue: 0,0:05:37.34,0:05:42.52,Default,,0000,0000,0000,,Then, you get to\Npositive 1, positive 2.
Dialogue: 0,0:05:42.52,0:05:44.94,Default,,0000,0000,0000,,And then you have negative 1.
Dialogue: 0,0:05:44.94,0:05:47.23,Default,,0000,0000,0000,,And you have negative 2.
Dialogue: 0,0:05:47.23,0:05:49.72,Default,,0000,0000,0000,,And then on the x-axis,\Nit's all positive.
Dialogue: 0,0:05:49.72,0:05:53.18,Default,,0000,0000,0000,,And I'll let you think about\Nwhether the domain here
Dialogue: 0,0:05:53.18,0:05:56.08,Default,,0000,0000,0000,,is-- well, when you\Nthink about it--
Dialogue: 0,0:05:56.08,0:05:58.27,Default,,0000,0000,0000,,is a logarithmic\Nfunction defined
Dialogue: 0,0:05:58.27,0:06:03.05,Default,,0000,0000,0000,,for an x that is not positive?
Dialogue: 0,0:06:03.05,0:06:07.19,Default,,0000,0000,0000,,So is there any power that I can\Nraise five to that I can get 0?
Dialogue: 0,0:06:07.19,0:06:08.37,Default,,0000,0000,0000,,No.
Dialogue: 0,0:06:08.37,0:06:11.12,Default,,0000,0000,0000,,You could raise five to an\Ninfinitely negative power
Dialogue: 0,0:06:11.12,0:06:13.72,Default,,0000,0000,0000,,to get a very, very, very, very\Nsmall number that approaches
Dialogue: 0,0:06:13.72,0:06:15.84,Default,,0000,0000,0000,,zero, but you can\Nnever get-- there's
Dialogue: 0,0:06:15.84,0:06:18.26,Default,,0000,0000,0000,,no power that you can\Nraise 5 to to get 0.
Dialogue: 0,0:06:18.26,0:06:19.80,Default,,0000,0000,0000,,So x cannot be 0.
Dialogue: 0,0:06:19.80,0:06:21.59,Default,,0000,0000,0000,,And there's no power\Nthen you could raise 5
Dialogue: 0,0:06:21.59,0:06:24.03,Default,,0000,0000,0000,,to get another negative number.
Dialogue: 0,0:06:24.03,0:06:25.78,Default,,0000,0000,0000,,So x can also not be\Na negative number.
Dialogue: 0,0:06:25.78,0:06:28.16,Default,,0000,0000,0000,,So the domain of this function\Nright over here-- and this
Dialogue: 0,0:06:28.16,0:06:30.41,Default,,0000,0000,0000,,is relevant, because we want\Nto think about what we're
Dialogue: 0,0:06:30.41,0:06:33.50,Default,,0000,0000,0000,,graphing-- the domain here is\Nx has to be greater than zero.
Dialogue: 0,0:06:33.50,0:06:35.23,Default,,0000,0000,0000,,Let me write that down.
Dialogue: 0,0:06:35.23,0:06:39.68,Default,,0000,0000,0000,,The domain here is that x\Nhas to be greater than 0.
Dialogue: 0,0:06:39.68,0:06:41.30,Default,,0000,0000,0000,,So we're only going\Nto be able to graph
Dialogue: 0,0:06:41.30,0:06:45.66,Default,,0000,0000,0000,,this function in\Nthe positive x-axis.
Dialogue: 0,0:06:45.66,0:06:48.38,Default,,0000,0000,0000,,So with that out of the\Nway, x gets as large as 25.
Dialogue: 0,0:06:48.38,0:06:51.15,Default,,0000,0000,0000,,So let me graph-- we\Nput those points here.
Dialogue: 0,0:06:51.15,0:06:57.43,Default,,0000,0000,0000,,So that is 5, 10,\N15, 20, and 25.
Dialogue: 0,0:06:57.43,0:06:58.88,Default,,0000,0000,0000,,And then let's plot these.
Dialogue: 0,0:06:58.88,0:07:00.05,Default,,0000,0000,0000,,So the first one is in blue.
Dialogue: 0,0:07:00.05,0:07:02.72,Default,,0000,0000,0000,,When x is 1/25 and\Ny is negative 2--
Dialogue: 0,0:07:02.72,0:07:06.09,Default,,0000,0000,0000,,When x is 1/25 so\N1 is there-- 1/25
Dialogue: 0,0:07:06.09,0:07:09.94,Default,,0000,0000,0000,,is going to be really close to\Nthere-- Then y is negative 2.
Dialogue: 0,0:07:09.94,0:07:12.68,Default,,0000,0000,0000,,So it's going to be\Nlike right over there,
Dialogue: 0,0:07:12.68,0:07:14.19,Default,,0000,0000,0000,,not quite at the y-axis.
Dialogue: 0,0:07:14.19,0:07:17.04,Default,,0000,0000,0000,,We're at 1/25 to the\Nright of the y-axis.
Dialogue: 0,0:07:17.04,0:07:17.100,Default,,0000,0000,0000,,But pretty close.
Dialogue: 0,0:07:17.100,0:07:19.12,Default,,0000,0000,0000,,So that's right over there.
Dialogue: 0,0:07:19.12,0:07:23.68,Default,,0000,0000,0000,,That is 1 over 25, comma\Nnegative 2 right over there.
Dialogue: 0,0:07:23.68,0:07:26.27,Default,,0000,0000,0000,,Then, when x is one\Nfifth, which is slightly
Dialogue: 0,0:07:26.27,0:07:30.55,Default,,0000,0000,0000,,further to the right, one\Nfifth y is negative 1.
Dialogue: 0,0:07:30.55,0:07:32.88,Default,,0000,0000,0000,,So right over there.
Dialogue: 0,0:07:32.88,0:07:36.95,Default,,0000,0000,0000,,So this is one\Nfifth, negative 1.
Dialogue: 0,0:07:36.95,0:07:40.29,Default,,0000,0000,0000,,Then when x is 1, y is 0.
Dialogue: 0,0:07:40.29,0:07:43.31,Default,,0000,0000,0000,,So 1 might be right there.
Dialogue: 0,0:07:43.31,0:07:46.55,Default,,0000,0000,0000,,So this is the point 1,0.
Dialogue: 0,0:07:46.55,0:07:50.63,Default,,0000,0000,0000,,And then when x is 5, y is 1.
Dialogue: 0,0:07:50.63,0:07:53.18,Default,,0000,0000,0000,,When x is 5, I covered it\Nover here, when this is five,
Dialogue: 0,0:07:53.18,0:07:56.53,Default,,0000,0000,0000,,y is 1.
Dialogue: 0,0:07:56.53,0:07:59.28,Default,,0000,0000,0000,,So that's the point 5,1.
Dialogue: 0,0:07:59.28,0:08:02.20,Default,,0000,0000,0000,,And then finally,\Nwhen x is 25, y is 2.
Dialogue: 0,0:08:02.20,0:08:08.06,Default,,0000,0000,0000,,
Dialogue: 0,0:08:08.06,0:08:11.14,Default,,0000,0000,0000,,So this is 25,2.
Dialogue: 0,0:08:11.14,0:08:13.05,Default,,0000,0000,0000,,And then I can\Ngraph the function.
Dialogue: 0,0:08:13.05,0:08:17.03,Default,,0000,0000,0000,,And I'll do it-- let me do it\Nin a color-- I'll use this pink.
Dialogue: 0,0:08:17.03,0:08:23.55,Default,,0000,0000,0000,,So as x gets super, super,\Nsuper, super small, y goes
Dialogue: 0,0:08:23.55,0:08:25.82,Default,,0000,0000,0000,,to negative infinity.
Dialogue: 0,0:08:25.82,0:08:30.49,Default,,0000,0000,0000,,It gets really small-- to\Nget x's or as x becomes--
Dialogue: 0,0:08:30.49,0:08:34.18,Default,,0000,0000,0000,,if you say what power do\Nyou have to raise 5 to
Dialogue: 0,0:08:34.18,0:08:36.54,Default,,0000,0000,0000,,to get 0.0001?
Dialogue: 0,0:08:36.54,0:08:38.53,Default,,0000,0000,0000,,It has to be very, very,\Nvery negative power.
Dialogue: 0,0:08:38.53,0:08:43.09,Default,,0000,0000,0000,,So y is going to be very\Nnegative as we approach 0.
Dialogue: 0,0:08:43.09,0:08:47.39,Default,,0000,0000,0000,,And then it kind of\Nmoves up like that.
Dialogue: 0,0:08:47.39,0:08:53.11,Default,,0000,0000,0000,,And then starts to kind of\Ncurve to the right like that.
Dialogue: 0,0:08:53.11,0:08:54.84,Default,,0000,0000,0000,,And this thing\Nright over here, is
Dialogue: 0,0:08:54.84,0:08:58.89,Default,,0000,0000,0000,,going to keep going down at\Na steeper and steeper rate.
Dialogue: 0,0:08:58.89,0:09:03.16,Default,,0000,0000,0000,,And it's never going\Nto quite touch.
Dialogue: 0,0:09:03.16,0:09:04.06,Default,,0000,0000,0000,,the y-axis.
Dialogue: 0,0:09:04.06,0:09:06.37,Default,,0000,0000,0000,,It's going to get closer\Nand closer to the y-axis.
Dialogue: 0,0:09:06.37,0:09:09.84,Default,,0000,0000,0000,,But it's never going\Nto be quite touch it.