Slant ( oblique) Asymptote

A slant asymptote for a function is a slant straight line ( that’s either straight line through the origin or a straight line intersecting the axes at distinct points) which the function follows getting arbitrary closer to as x increases with no bound and as x decreases with no bound. Thus a rational function cannot have both slant and horizontal asymptote(If it has one, then it cannot have the other)

We already know that a rational function f(x) = p(x) / q(x), where p(x) and q(x) are polynomials with no common factors, has vertical asymptotes for all x satisfying q(x)=0, and a horizontal asymptote only if the degree of p(x) is either equal or less than the degree of q(x). If the degree of p(x) = 1 + the degree of q(x), then f will have a slant asymptote.

Finding the Slant Asymptote Example (1)

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Example (2)

Algebraic Tricks Examples

Long Division

Example (1)

Example (2)

Example (3)