MATH 133 -- Intensive Calculus for Science
September 21, 2005
An "interesting" rational function:
The numerator factors as ( x - 1)( x - 2), so the
graph will have x- axis intercepts at x = 1,2.
The denominator factors as ( x + 3)( x - 3) , so the
graph will have vertical asymptotes at x = -3, 3.
The ``end behavior'' (as
and
) can
be seen by multiplying top and bottom by 1/
-> 1.
Here's a Maple plot where we specify the ranges
of x- and y- values to plot, and tell Maple
to watch out for the vertical asymptotes:
> | plot((x^2-3*x+2)/(x^2-9),x=-4..4,y=-10..10,discont=true); |
Kind of hard to tell there are x- axis intercepts, isn't it. Let's try ``zooming in'':
> | plot((x^2-3*x+2)/(x^2-9),x=0..3,y=-1..1,discont=true); |
That's better!