Question

Consider the function f(x)=(x^2 -16)/(x-2). Determine all asymptotes of this function including horizontal, vertical, and oblique (slant).

Answer 1

any vertical asymptotes will occur at the zeros for the function in the denominator, so long they don't make the numerator =0
thus
x-2 =0 => x = 2

so the vertical asymptote is at x = 2

the degree of the numerator polynomial is greater than that of the denominator, that means there's no horizontal asymptote

Answer 2

because the degree of the numerator is greater than that of the denominator
it has no horizontal asymptote BUT it has a SLANT or OBLIQUE asymptote
whose equation is the quotient of the division of the both the numerator and denominator