00:01
All right, we're looking at a piecewise function, and we want to think about how we would describe it over each interval.
00:06
So let's think about our total f of x, and this is three different parts.
00:16
So in the first part, we know that it's going from where x is greater than or equal to negative six.
00:24
So negative six to x.
00:27
And then it is less than or equal to negative 2 because of that closed circle.
00:33
So our graph we can see is increasing over the interval.
00:40
So going up, goes up a total of four units, and then it goes over a total of four units.
00:51
So our slope is equal to one, which is pretty straightforward.
00:57
Really, really nice.
00:59
So our slope is one.
01:01
And then when we want to come up with our y intercept, we can just kind of continue this line, knowing that the slope is one, and we see that it's going to go right through where the y intercept is, is six.
01:12
So we get y is equal to 1x, because our slope is 1, plus 6, and that would be our function for over the, over the stretch of when x is equal to negative 6 or less than or equal to negative 2.
01:33
The next stretch is from when x is greater than negative 2, not equal to, just greater than, and less than or equal to positive 1.
01:49
Again, that has to do with that open circle under negative 2 and then the close circle on 1.
01:55
And what we see on this function, is that it's just a horizontal line.
02:01
And this horizontal line is right where y equals three.
02:03
So really all we have to say is y equals three, or f of x equals three.
02:13
And then the last interval, it's going from when x is greater than, same thing as kind of the one above it, x is greater than one, but then it is less than or equal to, six...