00:01
In this activity, we're being asked to explain why a given situation is represented by a continuous or a discontinuous function.
00:12
And the first situation we're given is the temperature at a specific location as a function of time.
00:19
Well, if i think about that graph, i've got time in seconds, minutes, hours.
00:28
I've got temperature in degrees, fahrenheit, kelvin, celsius, and time is continuous.
00:37
Time just happens.
00:40
We're not going to all of a sudden jump from one time to another.
00:44
And temperature also has to be continuous.
00:47
So as time passes, the temperature may get warmer, it may get cooler, it may get warmer again, but there is never a circumstance where the temperature is going to stop.
01:02
And then all of a sudden leap to a completely different temperature, that will not happen.
01:16
So temperature as a function of time is continuous.
01:24
And then we're asked for a situation where at a specific time the temperature is measured as a function of the distance from new york city going to west.
01:40
Well, if i consider a map, i've got new york city here, and i am looking due west, and as i travel further and further west, i am recording the temperature.
01:59
I've got a similar situation.
02:01
If i'm going to graph that, my input axis is going to be distance d.
02:10
My output is going to be temperature t.
02:15
I'm not all of a sudden going to jump from one place to another, so distance is continuous.
02:22
And as i travel along the temperature at one place is going to gradually change.
02:31
So the temperature right at new york city may be fairly warm.
02:36
As i cross the river, it may cool off.
02:39
As i head back into the mainland, it may get warmer again.
02:43
As i get higher in elevation, it may cool off, but the temperature is going to change gradually.
02:48
Again, there are not going to be any sudden jumps from one temperature to another without passing through all of the temperatures in between.
02:57
So that is also continuous.
03:00
Then we're being asked to look at a function, consider a function, the altitude above sea level as a function.
03:10
Of distance due west from new york city.
03:19
So i can think about my same map.
03:20
If i am starting at new york and i am traveling due west, i don't have a map handy.
03:32
But if i were to graph that, d is my distance.
03:39
I'm going to use e for elevation above sea level.
03:46
New york city is about right at sea level...