00:01
So for this problem, i'm given a rational function, and i want to find the domain, the vertical, and horizontal asymptotes.
00:10
So let's start with the domain.
00:12
In order to find the domain, i need to find where this function is defined, but i can't do that until i rewrite this.
00:19
So i'm going to simplify this expression into a 3 plus 1 over x squared, and now i need to find a common denominator.
00:29
So my common denominator is x squared.
00:35
So i need to change my numerator of the three as well, because whatever i multiply my denominator by, i need to multiply my numerator by as well.
00:44
And my second numerator stays the same.
00:47
So this gives us 3x squared plus 1 over x squared is our function, f of x.
00:56
So in order to find the domain, i need to find where my function is not defined.
01:04
So with a rational function, that's always going to be where the denominator equals zero.
01:09
So i'm going to set x squared equal to zero and then solve that for x, which just gives me x equals zero.
01:18
So i know my domain is going to be all real numbers except zero.
01:30
Okay...