Question 1113031: Can someone help? Tank you.
Find the equation of rational function f(x) with a removable discontinuity at x=-2, an infinite discontinuity at x=-3, an x intercept (-1,0), and y intercept (0,6).
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
A rational function with a removable discontinuity at a point  has a factor of  in BOTH the numerator and denominator. A rational function with an infinite discontinuity at a point has a factor of in the denominator ONLY. A rational function with an  -intercept at ) has a factor of in the numerator only.
Hence,  must be in both numerator and denominator,  must be in the denominator only, and  must be in the numerator only, thus:
\ =\ \frac{(x\ +\ 1)(x\ +\ 2)}{(x\ + \ 2)(x\ +\ 3))
And we are almost there. Note that \ =\ \frac{1}{3}) , but we want the  -intercept, that is the point \)) to be ) .
Hence, we need a lead coefficient of 18 to complete all of the given specifications.
\ =\ \frac{18(x\ +\ 1)(x\ +\ 2)}{(x\ + \ 2)(x\ +\ 3))
You don't specify the required form for your final answer so this form fits the requirements of the problem as you posted it. If you need it multiplied out, I'll just leave that in your capable hands.
John
My calculator said it, I believe it, that settles it
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