+1904 Is it possible for an equation to have a vertical, a horizontal, and an oblique asymptote? If yes, please provide an example of an equation where that will happen and show a graph. If no, if possible, please provide a reason why this cannot happen.
+128570 Assumng that we are talking about rational functions, it is not possible for a function to have a horizontal asymptote and an oblique asymptote at the same time. The reason for this is that a horizontal asymptote will occur when we have the same degree polynomial in the numerator as in the denominator. A slant asymptote will occur when the degree of the polynomial in the numerator is greater than the degree of the polynomial in the denominator.......thus we can have the following combo possibilities :
vertical asymptote / horizontal asyptote ....example [ x+ 3] / [x - 1]
vertical asymptote / slant asymptote ...... example [ x^2] / [ x - 1]
