Rational Functions with Oblique Asymptotes (AQA A-Level Further Maths): Flashcards

Slant asymptotes

Function is improper (num. degree ≥ denom. degree)

Numerator degree < denominator degree

Numerator degree ≥ denominator degree

Horizontal asymptote at $y = 0$

Use algebraic long division

The quotient $g(x)$ from long division

As $x \to \pm\infty$, remainder $\frac{r(x)}{d(x)} \to 0$

Solve denominator = 0

Multiply asymptote by denominator, compare to numerator