Finding vertical asymptotes...

• factor everything and reduce
• if the denominator just goes away, it's a hole, not an asymptote
• if the denominator is 0, the x value that made it so is the vertical asymptote

Finding horizontal asymptotes...

The algebra II way:

Where

• n is the degree of the numerator
• m is the dgree of the denominator

If

• n < m, horizontal asymptote -> y=0
• n = m, horizontal asymptote -> ratio of leading coefficients
• n > m, horizontal asymptote -> no horizontal asymptote

The (later) calculus way

• find the largest term in the denominator
• divide numerator and denominator by that largest term
• evalate limit of each as x -> ∞
• if evalation yields a constant, then y = that constant is the horizontal asymptote
• if not a constant, there are no horizontal asymptotes