graph from asymptotes
posted by Jen on .
Is it possible to roughly sketch a graph(without plotting the points) from the asymptotes of a rational function? Is yes, what are the rules?
For example, if I have to sketch a graph of y = (2x^2+10x-12)/x^2+x-6), how do I do it?
I got the vertical asymptotes as x=-3 & x=2, and horizontal asymptote y=2.
How do I draw a graph of this function without plotting points?
Factor the numerator and denominator.
find the roots of the numerator...that is where the graph will cross x axis.
Find the roots of the denomiantor, those are the points where y will be +- inf
sketch in the horizontal asy...
Now SKETCH in the missing areas.