00:01
So we're looking at the discontinuities here.
00:02
So let's go ahead and see what we got here.
00:04
So what we do here is we're going to look for, we need to factor our equations out.
00:11
So we can see what kind of discontinuity have.
00:14
Already i'm looking at one, we can see there's going to be a discontinuity here because the denominator is going to be zero when x is one.
00:22
So that's not going to work.
00:23
So let's just for the sake of doing this out, let's factor these.
00:30
So we get x plus one.
00:31
It's a difference of squares.
00:32
So we get that.
00:36
The numerator is going to cancel out.
00:39
So we get one over x plus one.
00:44
So what this tells us is there is a hole because this cancels out.
00:50
And we put x as 1 in.
00:52
When we let x be 1, we get 1 plus 1, which is 1 half.
00:59
And so the limit will be a half, however, is going to be a whole when x is 1.
01:06
So there's a hole.
01:19
Let's see for two.
01:20
We're going to do the same thing.
01:21
We have a negative value.
01:23
We can't just plug three in because we get zero.
01:26
So let's factor the numerator.
01:29
We get x minus three times x plus or x minus one over x minus three.
01:40
Those are going to cancel out.
01:42
So that means there's going to be a hole there because this is going to be negative x minus one.
01:49
We substitute 3 in for x and we get what's the value there we get negative what 4 negative 4 so that's the value there so there's going to be a whole so the the function will have an output of negative 4 there however there's a whole at negative 3 i think it's also called a jump no area there's like a just discontinuous there is a whole.
02:27
X is one, x is three, excuse me.
02:32
Same thing.
02:34
Factor the numerator.
02:37
X plus two, x.
02:40
And by the denominator, usually these problems, the denominator tells you what factors you're going to have in the numerator.
02:47
That's a little trick i've learned over the years.
02:50
I get x plus two.
02:53
Those cancel out.
02:54
So that tells us there's going to be a hole at negative...