Curve Sketching 2 (AQA A-Level Further Maths): Quizzes

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Rational Functions with Oblique Asymptotes
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When does a rational function have an oblique asymptote?

When numerator degree ≥ denominator degree

What is a proper rational function?

Numerator degree < denominator degree

After dividing to get y=g(x)+r(x)d(x)y = g(x) + \frac{r(x)}{d(x)}, what is the oblique asymptote equation?

y=g(x)y = g(x)

How do you find vertical asymptotes of a rational function?

Solve denominator = 0

What happens to r(x)d(x)\frac{r(x)}{d(x)} as x±x \to \pm\infty?

It approaches 0

What type of asymptote does a proper rational function typically have?

Horizontal at y=0y = 0

To find unknowns given an oblique asymptote, what should you do first?

Multiply asymptote by denominator

What should you ignore when stating the oblique asymptote equation?

The remainder

If numerator degree equals denominator degree, what type of asymptote occurs?

Oblique

What method is used to find oblique asymptotes?

Algebraic long division

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