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Calculus/Find the asymptotes and intercepts of the function and graph it

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Expert: - 11/28/2008


Question
f(x)=(2x squared +7)/(x squared +x-6)



I have no idea how to do this.

Answer
The assymptotes usually occur where the denominator is zero.
Set x² + x - 6 = 0 and solve for x.  It factors into
(x+3)(x-2), so set that equal to 0 and solve for the two values of x.

Since the x² is always positive, 2x² is always positive, and therefore 2x²+7 is always positive, so the numerator gives us nothing to be concerned about.  This means that your two x values are the solution for the vertical assymptotes.

Since the numerator is always positive, there are no zeros.

There is one linear assymptote.  Divided the top and bottom of the equation by x².  This will be the m in the equation y=mx, the slanted assymptote.

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