00:01
So in this question, we're going to determine the values of x where the function f of x is not continuous, and we're going to label each discontinuity as removable, jump, or infinite.
00:11
And this didn't really copy very well, but it appears that my function f of x is equal to one -half x plus five when x is less than or equal to two.
00:27
And it's x plus three when x is greater than two.
00:32
Now in the future is probably better for you to take pictures and upload them as opposed to cut and paste because cut and paste just doesn't come through very well in numerate.
00:43
So where am i worried about the continuity? i'm worried about continuity at x equals 2 at the break point between the two functions.
00:55
And so i ask myself, do we have continuity at x equals 2? well, in order to be continuous at x equals 2, i need the limit as x approaches 2 from the left, and the limit as x approaches 2 from the right of this function to be the same.
01:18
So let's first consider the limit as x approaches 2 from the left of this function.
01:26
Well, if i'm looking at the limit as x approaches 2 from the left, which piece of the function am i using when x is approaching 2 from the left? well, if x is approaching two from the left, my x values are less than two.
01:43
And so i would be using the piece of function, one -half x plus five.
01:50
To evaluate this limit, what do i do? i plug in.
01:56
And i get one -half times two plus five.
02:02
I get one plus five.
02:05
I get six.
02:06
Okay? that's my limit as x approaches two from the left of f of x...