00:01
We're going to graph the function, y is equal to x over x squared minus 9.
00:07
And so if we factor this, we get x plus 3, x minus 3.
00:14
And so by factoring it, that helps us find where the asymptotes will be.
00:19
Because we can see when x is equal to 3, we're going to divide by 0.
00:25
And so that would cause this vertical isotope.
00:29
And when x is negative 3, we will also divide by 0.
00:33
Which is another variable.
00:37
And next what we can do is we can play out where our horizontal asymptote will be.
00:43
So our horizontal asymptote, we only care about the values of x.
00:49
And so when x is very large, our function approximates x over x squared, which is 1 over x.
00:57
And so this goes to 0 when x is large.
01:01
So that means our horizontal asymptote for large values of x, will be 0.
01:11
Okay, so now let's figure out what happens between negative 3 and 3.
01:15
Well, we see it would cross the y intercept at 0, because when we plug in x is 0, we just get 0.
01:25
Now if we plug in a value to the left of that, let's say negative 1...