The question is for any rational function. I give one example in picture below. There we can see that first part of the "rule" is true. we indeed have vertical asymptotes at every x value where denominator is zero in this case x = 3 and x = 1. but second part of the rule is not true. we can see that if we inverse x ( we have factor that looks like a - x we get positive function between asymptotes.
