Question

Consider the function f(x) = (x^2-9)/(x-4) . Determine all asymptotes of this function including horizontal, vertical, and oblique (slant)

Answer 1

the vertical asymptote is found by solving

x - 4 = 0

which is the denominator.... having a zero denominator results in an undefined function.

an easy way to find the horizontal/oblique asymptote is using polynomial division



the quotient will be the equation of the asymptote and the remainder is ignored.