SOLUTION: Find a rational function the satisfies the given conditions. Answers may vary but try to give the simplest answer possible. Vertical asymptotes x=-2, x=5; x-intercept (4, 0)

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Question 137547: Find a rational function the satisfies the given conditions. Answers may vary but try to give the simplest answer possible.
Vertical asymptotes x=-2, x=5; x-intercept (4, 0)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find a rational function that satisfies the given conditions. Answers may vary but try to give the simplest answer possible.
Vertical asymptotes x=-2, x=5 means (x+2) and (x-5) in the denominator
x-intercept (4, 0) means f(4)=0
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EQUATION:
f(x) = a/[(x+2)(x-5)]
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To keep the function from crossing the x-axis at other than (4,0)
let "x^2-1" be in the numerator so you have a horizontal asymptote
at y = 1
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EQUATION:
f(x) = (ax^2-1)/[(x+2)(x-5)]
f(4) = (16a-1)/[6*-1] = 0
Then 16a-1 = 0
a = (1/16)
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EQUATION:
f(x) = ((1/16)x^2 -1)/[(x+2)(x-5)]

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Cheers,
Stan H.