Question

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

Answer 1

Answer:

• 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.