Find any values such that is undefined, that is such that the denominator function is equal to zero. Then the vertical line is a vertical asymptote.
Determine the degree of each of the numerator polynomial and the denominator polynomial.
If the degree of the denominator is greater than the degree of the numerator, then the horizontal axis of the coordinate system is an asymptote.
If the degree of the denominator is one less than the degree of the numerator, there is an oblique asymptote which equation is the quotient, excluding the remainder obtained by polynomial long division of the numerator by the denominator.
If the degreesof the numerator and denominator are equal, there is a horizontal asymptote at the horizontal line where is the lead coefficient of the numerator and is the lead coefficient of the denominator.
My calculator said it, I believe it, that settles it