00:01
Alright, so here's this rational function and they want us to graph all the vertical and horizontal asymptotes.
00:07
Okay, well to find the horizontal asymptote, this thing, we just look and realize, oh, they're both x squareds, so we make a fraction out of the leading coefficients of the first terms, so we know the horizontal asymptote's going to be y equals negative a half.
00:29
So when we graph this thing, so here's negative one, two, three, four, five, one, two, three, four, five, so here's a little quickie graph, so at negative a half, that's going to be right here, right about here, this is the horizontal asymptote, that's the line, whoops, y equals negative a half.
01:09
Alright, now let's talk about the vertical asymptotes.
01:18
The vertical asymptotes are going to happen where the denominator is equal to zero.
01:23
It's where two x squared plus three equals zero, but if we try and solve this, two x squared equals negative three, divide by two, x squared equals negative three halves, when we go to take the square root, you know, we get imaginary, get an error, right? so there's going to be no vertical asymptotes, because we can't take the square root of a negative.
02:03
Basically, this is a parabola, it's always positive, it's never going to be negative, it's never going to equal zero...