Put the function in the form (y=f(x)).
Check whether ( deg(text{numerator}) = deg(text{denominator}) + 1 ); if yes, a slant (oblique) asymptote may exist.
If the function is a rational function, perform polynomial long division of the numerator by the denominator.
Let the quotient be (Q(x)) (a first-degree polynomial) and the remainder be (R(x)) over the denominator.
The slant asymptote is (y = Q(x)).
If the degrees differ by more than 1, no slant asymptote of the form (y=ax+b) exists (for rational functions).
Verify by checking (lim_{xtopminfty}left(f(x)- (ax+b)right)=0) for (y=ax+b).
For non-rational functions, attempt to find (ax+b) by computing limits of the form (a=lim_{xtopminfty}frac{f(x)}{x}) (if it exists), then (b=lim_{xtopminfty}(f(x)-ax)) (if it exists).
Confirm the result with (lim_{xtopminfty}left(f(x)-(ax+b)right)=0).