Some rational functions do not level off — they chase a slanted line forever. When the numerator's degree is exactly one higher than the denominator's, long division splits the function into a linear part plus a remainder fraction that fades to zero, and that line is the oblique (slant) asymptote. For (x² + 3x + 2)/(x + 1), division gives x + 2 with a zero remainder — the graph hugs the line y = x + 2 at the extremes while wiggling near the middle.

US calculus students meet slant asymptotes right after horizontal ones, and the distinction is a favorite exam question: equal degrees give a horizontal asymptote at the ratio of leading coefficients, numerator-one-higher gives a slant line, and anything steeper gives a curvy "asymptotic" shape instead. The asymptote describes end behavior — where the function is headed as x grows large — which is exactly what you need for sketching and for understanding long-run trends in rational models. This calculator evaluates the division's linear quotient: enter the quotient's slope and intercept contributions and it returns points on the asymptote line for your graph.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Oblique Asymptote Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.