00:01
For this function, this rational, where we have x plus 2, x minus 3 in the numerator, just double checking, as well as x plus 5, x minus 1 in the denominator.
00:18
And to start with the first part, a, with the vertical asymptotes, i like to remind students that it's the non -cancelling factors in the denominator.
00:28
Denominator.
00:32
So non -cancelling and on bottom.
00:35
And you can set each piece equal to zero, although most of my students just haven't memorized that if it's a factor, the vertical asymptote would be the opposite.
00:47
So you subtract five over, same thing with x minus one.
00:50
The reason why you can just do the opposite, you have to do the inverse operation.
00:55
So there's part a, part b, the x intercept, well, the x intercept would be where y equals zero.
01:07
So that's a non -canceling in the numerator.
01:11
Oops, totally misspelled that.
01:18
Now, the reason why i talk about non -cancelling is if they cancel, it's actually not a vertical asymptote or an x intercept, it's actually what we consider it a whole.
01:28
So x plus 2 equal to 0 and x minus 3, but again, it's going to be the opposite because you subtract two over or you add three.
01:38
So that's part b.
01:40
Part c, as for the horizontal asthmpton.
01:43
This is a little bit trickier...