Posted by **Jen** on Sunday, February 4, 2007 at 12:34pm.

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?

Thanks

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.

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