Discover the oblique (slant) asymptote of rational functions instantly. This calculator simplifies the process of finding the linear asymptote when the degree of the numerator is exactly one greater than the denominator's, providing a clear understanding of function behavior at infinities. Ideal for students and professionals.
Formula:
An oblique (or slant) asymptote exists for a rational function, f(x) = N(x) / D(x), when the degree of the numerator, N(x), is exactly one greater than the degree of the denominator, D(x).
In such cases, polynomial long division yields f(x) = Q(x) + R(x) / D(x), where Q(x) is the quotient (a linear polynomial), and R(x) is the remainder. The oblique asymptote is given by y = Q(x).
For a rational function of the form f(x) = (ax2 + bx + c) / (dx + e), where a ≠ 0 and d ≠ 0, the oblique asymptote is given by the equation:
y = (a/d)x + (b - ae/d)/d
Where:
- a: Coefficient of x2 in the numerator.
- b: Coefficient of x in the numerator.
- c: Constant term in the numerator.
- d: Coefficient of x in the denominator.
- e: Constant term in the denominator.