<Dd> y = x 3 + 2 x 2 + 3 x + 4 x (\ displaystyle y = (\ frac (x ^ (3) + 2x ^ (2) + 3x + 4) (x))) </Dd> <P> has a curvilinear asymptote y = x + 2x + 3, which is known as a parabolic asymptote because it is a parabola rather than a straight line . </P> <P> Asymptotes are used in procedures of curve sketching . An asymptote serves as a guide line to show the behavior of the curve towards infinity . In order to get better approximations of the curve, curvilinear asymptotes have also been used although the term asymptotic curve seems to be preferred . </P> <P> The asymptotes of an algebraic curve in the affine plane are the lines that are tangent to the projectivized curve through a point at infinity . For example, one may identify the asymptotes to the unit hyperbola in this manner . Asymptotes are often considered only for real curves, although they also make sense when defined in this way for curves over an arbitrary field . </P>

When does a function not have a horizontal asymptote