00:01
Okay, we want to sketch the graph of a function f of x.
00:05
We want a removable discontinuity at 3 and the jump discontinuity at 5.
00:14
A removable discontinuity when x is 3.
00:20
So let's have an open circle right here at x equals 3.
00:25
And here's the graph of our function as x is approaching 3 from the left side.
00:31
Here is the graph of the function as x is approaching 3 from the positive side.
00:42
Now, let's define the function when x is 3 to be this point right here.
00:51
All right.
00:53
So this is what we would call a removable discontinuity at 3.
00:57
You can see that this function is discontinuous at 3 because as the function, as x approaches, three, okay, the function looks like it wants to approach this point, this value here.
01:13
Instead, the function is defined to be this value up here.
01:17
This is a removable discontinuity.
01:20
If we redefined f of x when x equals three to be this point, if we move this point of the function and put it here, then we would have a continuous function.
01:32
So that's why this is called a removable discontinuity.
01:37
A jump discontinuity at 5 is a little more serious...