SOLUTION: Write a rational function g with vertical asymptotes at x=3, x=-3, a horizontal asymptote at y=-2 and with no x intercept.

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Question 934457: Write a rational function g with vertical asymptotes at x=3, x=-3, a horizontal asymptote at y=-2 and with no x intercept.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given: vertical asymptotes at x=3, x=-3, a horizontal asymptote at y=-2 and with no x intercept:
Since g has a vertical asymptotes at x+=+3 and x+=+-3, then the denominator of the rational function contains the product of %28x+-3%29 and %28x+%2B+3%29. Function g has the form:
g%28x%29+=+h%28x%29+%2F%28+%28x-3%29%28x+%2B+3%29%29
For the horizontal asymptote to exist, the numerator of . At the same time the numerator of g%28x%29+has+%7B%7B%7Bno real zeros.
Hence
f%28x%29+=+%28-2x%5E2+-6+%29+%2F+%28+%28x+-3%29%28x+%2B+3%29+%29