SOLUTION: Please help me with: Find a rational function that has x=4 and x=3 as vertical Asymptotes, and (-2,0) as an x-intercept. Thanks

Algebra ->  Rational-functions -> SOLUTION: Please help me with: Find a rational function that has x=4 and x=3 as vertical Asymptotes, and (-2,0) as an x-intercept. Thanks       Log On


   

Question 166599: Please help me with:
Find a rational function that has x=4 and x=3 as vertical Asymptotes, and (-2,0) as an x-intercept.
Thanks
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
if you want vertical asymptotes at x = 3 and x = 4, then you need to have f(x) = infinity when x = 3, or when x = 4.
this happens if the denominator of a rational expression is 0.
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if you want x intercept of -2, then you need to make f(x) = 0 when x = -2.
this happens when the numerator of a rational expression is 0.
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an equation that satisfies both conditions would be:
f%28x%29+=+%28x%2B2%29%2F%28%28x-3%29%2A%28x-4%29%29
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when x = -2, the numerator of (x+2) equals 0.
when x = 3, or when x = 4, the denominator of (x-3)*(x-4) = 0.
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a graph of that equation looks like this:
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graph+%28800%2C800%2C-5%2C10%2C-1%2C1%2C%28x%2B2%29%2F%28%28x-3%29%2A%28x-4%29%29%29