Determine the horizontal, vertical, and slant asymptotes: y=x2+2x-3/x-7

vertical asymptote: x = 7 slant asymptote: y = x+9

Step-by-step explanation:

The vertical asymptotes are found where a denominator factor is zero (and there is no corresponding numerator factor to cancel it). Here, that is at x = 7.

There is no horizontal asymptote because the numerator is of higher degree than the denominator.

When you divide the numerator by the denominator, you get ...

y = (x + 9) + 60 / (x - 7)

Then when x gets large, the behavior is governed by the terms not having a denominator: y = x + 9. This is the equation of the slant asymptote.