Oblique asymptotes of rational functionsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

When does a rational function have an oblique asymptote?
How do you find an oblique asymptote?
What happens to \frac{r}{q(x)} as |x|\to\infty?
Oblique asymptote of \frac{x^2+x-6}{x-1}?
Write \frac{x^2+x-6}{x-1} in divided form.
Horizontal asymptote when degrees are equal?
Horizontal asymptote when the numerator has lower degree?
Can a curve meet its oblique asymptote?
How do you decide if the curve is above or below the asymptote?
Where are the vertical asymptotes?
How many times does a line parallel to the oblique asymptote meet the curve?
Division form of \frac{x^2+ax+b}{x-1}?
How do you check a division?

Exam questions on Oblique asymptotes of rational functions

The curve $C$ has equation $y=\dfrac{x^2+x-6}{x-1}$ .
Show that $C$ lies below its oblique asymptote when $x>1$ .2 marks
The curve $C$ has equation $y=\dfrac{2x^2-3x+1}{x+2}$ .
Show that $C$ does not meet its oblique asymptote.2 marks
The curve $C$ has equation $y=\dfrac{2x^2+3}{x-1}$ .
Find the equations of all the asymptotes of $C$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).