00:01
Okay, we're going to take a look at a piecewise function that is defined as f of x is equal to negative 2 for x values less than or equal to negative 1, ax minus b for x values between negative 1 and 1, and 3 for x values greater than are equal to 1.
00:29
And what we want to determine is for what x, for what a and b values, will f of x be continuous for all x values? okay.
00:56
And what we do know is that in order for a function to be continuous, the one side of limits have to equal each other.
01:05
And so that's where we're going to start.
01:08
We're going to start with the limit as x approaches negative 1 from the left of negative 2.
01:16
That has got to equal the limit as x approaches negative 1 from the right of ax minus b.
01:27
And so we also know, since we have three partitions, that the limit as x approaches 1 from the 1 from the limit, the left, that of a, x minus b, that has got to equal the limit as x approaches one from the right of three.
01:50
And so now we're going to kind of solve these simultaneously.
01:53
So this is negative 2 is equal to negative a minus b.
02:03
And over here we get a minus b.
02:05
And over here we get a minus b.
02:09
Is equal to three.
02:12
So basically what we have is we have a system of equations that we're going to solve for a and b...