Slant Asymptote Formula
For a rational function f(x) of the form g(x)/h(x), the slant asymptote, S(x) is of the form:
S(x) =
The value of quotient S(x) is calculated using long division method for the dividend g(x) and divisor h(x).
Example: Obtain the slant asymptote for the function: y = (x2 – 3x – 10)/(x – 5).
Solution:
We have, f(x) = (x2 – 3x – 10)/(x – 5).
Here f(x) has a slant asymptote as the degree of numerator is one more than that of denominator.
Using the slant asymptote formula, we have
As the quotient obtained is x + 2, the slant asymptote for the given function f(x) is,
S(x) = x + 2
Slant Asymptote Formula
A rational function is a polynomial ratio in which the denominator polynomial should not be equal to zero. It is a function that is the polynomial ratio. A rational function is any function of one variable, x, that can be expressed as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0. There are three sorts of asymptotes for a rational function, that is, horizontal, vertical, and slant asymptotes.