Porisma

A hint to get started

Sketch rational curves from division and domain

Sketch the graph of the following curves, indicating clearly the coordinates of any intersections with the axes, turning points and the equations of any asymptotes:

(a) y=2x−3x−4y=\dfrac{2x-3}{x-4}.

(b) y=x2−2x2−1y=\dfrac{x^2-2}{x^2-1}.

(c) y=2x2−x+1x−2y=\dfrac{2x^2-x+1}{x-2}.

(d) y=x2−x−12x−2y=\dfrac{x^2-x-12}{x-2}.

(e) y=(x+5)2x2−5xy=\dfrac{(x+5)^2}{x^2-5x}.

CJC · Lecture · Example 9

Divide improper rational functions into polynomial plus proper remainder, then check poles, intercepts and derivative signs on each continuous branch.

Read the worked solution