Question 199802: what is the domain of h(x)0=-4x/(x-9)(x+8)
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! f(x) =y = (-4x) / { (x-9)(x+8)] = (-4x)/ ( x^2 -x-72)
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Vertical asymptotes at x=9,,,,x=-8,,,,zeros of the denominator
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horizontal asymptotes at y=0,,,,,leading exponent of num > dem
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x intercept at x=0,,,,,zeros of numerator
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Domain is all Real Numbers except at x=-8,,,and at x=9.
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To make a rough sketch,,,use x-y coordinate system,,
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starting at - infinity, y is just positive and curve upward as we move to right and
goes to + infinity at x=-8.
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On the other side of x=-8 (-7.9) y is at - infinity ,,,curves upward to (0,0) and then to
+ infinity, at x=9. Watch change of direction, double curve, close to (0,0)
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On the other side of x=9 ( x=9.1) y is at - infinity, and as we move to right it curves upward to approach y=0 on the negative side.
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