Question

How do you find vertical, horizontal and oblique asymptotes for `(2x^3 - 3x + 1) / (x^2 + 4)`?

Answer 1

V.A. none
H.A. none
O.A. y= 2x

Explanation:

• For a function to have vertical asymptote, the function needs to have undefined points also known as zeros of denominator
  this function is true and does not have any undefined points so there is no vertical asymptote

• If the degree of numerator > the degree of denominator, then there will be no horizontal asymptote
  In this function, the degree of the numerator is 3 and degree of denominator is 2, therefore this function has no horizontal asymptote

• To get the oblique/ slant asymptote use polynomial long devision
  

therefore the slant asymptote is y = 2x