AS/A2 Pure 1 Pure 2

P3 Topic 1: Algebra
Rational functions 4
The graph of the above rational function is shown. Initially, a=4, b=3. c=0 and d=2. Watch how the curve changes as a and b vary. Make a=4, b=3. c=0 and d=2 again and then vary c or d. Investigate the effect of changing a, b, c or d.

Summary When c=0 and d is positive there are no asymptotes Any asymptotes will occur when x2+ cx +d = 0 has solutions. This happens when c2-4d > 0 The curve crosses the x axis when x2+ ax +b = 0 has solutions, which is when a2-4b > 0 Based on free Java applets from JavaMath