WEBVTT
1
00:00:00.690 --> 00:00:02.940 A:middle L:90%
Hi, My name is Jeffrey and we'LL be doing
2
00:00:02.950 --> 00:00:06.320 A:middle L:90%
a problem from section one point one, number six
3
00:00:06.690 --> 00:00:09.949 A:middle L:90%
from Stuart's expeditions. In this section, we discuss
4
00:00:09.949 --> 00:00:13.779 A:middle L:90%
examples of ordinary everyday functions. Population is function of
5
00:00:13.779 --> 00:00:17.190 A:middle L:90%
time. Postage cost is a function of way water
6
00:00:17.190 --> 00:00:20.589 A:middle L:90%
temperatures of all time Give three examples of functions from
7
00:00:20.589 --> 00:00:23.539 A:middle L:90%
everyday life that are described verbally and what you see
8
00:00:23.539 --> 00:00:26.600 A:middle L:90%
about their domain and range and sketched a rough draft
9
00:00:26.609 --> 00:00:29.100 A:middle L:90%
if possible. Okay, so I had to cook
10
00:00:29.100 --> 00:00:31.059 A:middle L:90%
up three examples on my own, and one of
11
00:00:31.059 --> 00:00:34.520 A:middle L:90%
them is gonna include emptying a bathtub. So for
12
00:00:34.520 --> 00:00:37.130 A:middle L:90%
a number one here, emptying a bathtub is going
13
00:00:37.130 --> 00:00:41.539 A:middle L:90%
to be a function of heights over time. It
14
00:00:41.829 --> 00:00:48.119 A:middle L:90%
so height of the water as a function, Uh
15
00:00:48.350 --> 00:00:54.149 A:middle L:90%
, time. Okay. So in our graph here
16
00:00:54.149 --> 00:00:57.479 A:middle L:90%
, it looks like maybe if the heights, we're
17
00:00:57.479 --> 00:01:00.829 A:middle L:90%
to start at twenty four inches off the ground,
18
00:01:00.119 --> 00:01:03.109 A:middle L:90%
OK? And the water is going to drain at
19
00:01:03.120 --> 00:01:08.530 A:middle L:90%
a constant rate until the height of the water is
20
00:01:08.540 --> 00:01:12.750 A:middle L:90%
zero. Maybe it takes five minutes for that's happened
21
00:01:15.040 --> 00:01:15.549 A:middle L:90%
. You mean takes five minutes. What happened?
22
00:01:17.239 --> 00:01:19.829 A:middle L:90%
So it looks like we're gonna have ahh linear graph
23
00:01:19.829 --> 00:01:26.510 A:middle L:90%
here and the domain of this function will hate this
24
00:01:26.510 --> 00:01:30.680 A:middle L:90%
height function is gonna be the set of all acts
25
00:01:30.689 --> 00:01:36.250 A:middle L:90%
such that ex belongs from time zero Teo five minutes
26
00:01:38.469 --> 00:01:42.959 A:middle L:90%
and the range of the height function here. Correspondence
27
00:01:42.959 --> 00:01:47.629 A:middle L:90%
tio the vertical axis, the height they will call
28
00:01:47.629 --> 00:01:49.329 A:middle L:90%
it. Why I said, Well, why such
29
00:01:49.329 --> 00:01:53.390 A:middle L:90%
that? Why belongs from zero inches off the ground
30
00:01:53.670 --> 00:02:00.609 A:middle L:90%
? Teo twenty four inches off. And so,
31
00:02:00.620 --> 00:02:05.109 A:middle L:90%
for our second example, I thought of the temperature
32
00:02:05.120 --> 00:02:08.490 A:middle L:90%
of and the temperature of the oven when baking cookies
33
00:02:09.219 --> 00:02:14.930 A:middle L:90%
. So, Theo, we're talking about temperature.
34
00:02:15.740 --> 00:02:22.830 A:middle L:90%
That's a function temperature as a function of time.
35
00:02:24.120 --> 00:02:30.129 A:middle L:90%
Okay, so I think home, you know,
36
00:02:30.139 --> 00:02:34.639 A:middle L:90%
it's usually around indoors at the home is usually around
37
00:02:34.689 --> 00:02:38.719 A:middle L:90%
No. Seventy four degrees, I'll say his seventy
38
00:02:38.770 --> 00:02:44.370 A:middle L:90%
degrees as it's pre pre heating. Uh, maybe
39
00:02:44.370 --> 00:02:46.419 A:middle L:90%
at a constant rate. Here is the supreme heat
40
00:02:46.419 --> 00:02:51.669 A:middle L:90%
up tio three hundred fifty degrees and maybe it takes
41
00:02:51.680 --> 00:02:53.629 A:middle L:90%
, I don't know, ten minutes for that there
42
00:02:54.120 --> 00:02:57.319 A:middle L:90%
, and we're baking cookies for I don't know.
43
00:02:57.319 --> 00:03:00.569 A:middle L:90%
Let's see twenty minutes so it stays at the temperature
44
00:03:00.569 --> 00:03:04.939 A:middle L:90%
of the oven, stays at three hundred fifty degrees
45
00:03:05.210 --> 00:03:07.530 A:middle L:90%
for twenty minutes, and then it needs to cool
46
00:03:07.530 --> 00:03:12.310 A:middle L:90%
down all the way back to temperature, which is
47
00:03:12.310 --> 00:03:15.979 A:middle L:90%
at seventy four threes. And maybe it takes just
48
00:03:15.979 --> 00:03:19.490 A:middle L:90%
this much time. So maybe this is it.
49
00:03:20.340 --> 00:03:25.389 A:middle L:90%
Minutes there, maybe two, three minute or to
50
00:03:25.389 --> 00:03:30.419 A:middle L:90%
cool down. So let's talk about the domain of
51
00:03:30.430 --> 00:03:34.039 A:middle L:90%
this temperature function, okay? And that's going to
52
00:03:34.039 --> 00:03:37.389 A:middle L:90%
be the set of all acts. Such that ex
53
00:03:37.389 --> 00:03:45.120 A:middle L:90%
belongs from zero Teo, uh, minutes for the
54
00:03:45.120 --> 00:03:50.479 A:middle L:90%
range Respons Teo, the temperature of the oven.
55
00:03:51.030 --> 00:03:53.509 A:middle L:90%
Hey. And so I guess the temperature of the
56
00:03:53.509 --> 00:03:58.569 A:middle L:90%
heaven belongs from seventy four degrees all the way.
57
00:03:58.580 --> 00:04:04.860 A:middle L:90%
Teo three hundred. And for this last one here
58
00:04:04.860 --> 00:04:08.370 A:middle L:90%
, I said, um, writing a bike down
59
00:04:08.370 --> 00:04:11.210 A:middle L:90%
the street. Okay. Riding a bike down the
60
00:04:11.210 --> 00:04:14.560 A:middle L:90%
street. So this is a function a speed over
61
00:04:14.560 --> 00:04:18.009 A:middle L:90%
time. Its speed is a function. Uh,
62
00:04:18.350 --> 00:04:23.779 A:middle L:90%
hi, Purses. So when I ride my bike
63
00:04:23.790 --> 00:04:28.149 A:middle L:90%
, I need t o start at, uh,
64
00:04:28.259 --> 00:04:30.089 A:middle L:90%
you know, my philosophy starts at zero. Obviously
65
00:04:30.100 --> 00:04:33.560 A:middle L:90%
and accelerate a little bit. So maybe it takes
66
00:04:33.569 --> 00:04:38.389 A:middle L:90%
Maybe I take off like this here, and I
67
00:04:38.399 --> 00:04:43.259 A:middle L:90%
reach a top speed of twenty miles per hour and
68
00:04:43.259 --> 00:04:46.620 A:middle L:90%
maybe I I stay at twenty miles per hour and
69
00:04:46.620 --> 00:04:47.350 A:middle L:90%
maybe I could get a little bit faster than that
70
00:04:47.600 --> 00:04:48.839 A:middle L:90%
. But then, at the end of the street
71
00:04:48.839 --> 00:04:51.100 A:middle L:90%
, I need Teo. Stop at the stop sign
72
00:04:51.100 --> 00:05:00.730 A:middle L:90%
. So there you are there. So the domain
73
00:05:00.730 --> 00:05:03.870 A:middle L:90%
of dysfunction will call it the domain of speech function
74
00:05:03.920 --> 00:05:09.079 A:middle L:90%
. Here s is this edible acts he reckons any
75
00:05:09.089 --> 00:05:12.870 A:middle L:90%
time such that Immediate. Oh, so maybe this
76
00:05:12.870 --> 00:05:16.649 A:middle L:90%
takes no three minutes or all of this event happened
77
00:05:17.139 --> 00:05:24.410 A:middle L:90%
. So explosions from zero to three minutes as I
78
00:05:24.420 --> 00:05:28.470 A:middle L:90%
ride my bike down the street and the range corresponds
79
00:05:28.470 --> 00:05:33.160 A:middle L:90%
to how fast I'm going, the speed you is
80
00:05:33.170 --> 00:05:35.800 A:middle L:90%
the center of all. Why such that? Why
81
00:05:35.810 --> 00:05:44.699 A:middle L:90%
along from zero miles per hour Tio watching.