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Question 1052179: Hello. I have been working on a 5 point graded homework or "exit card" for the past two hours or so and I just can't crack it. It asks me to create an equation where: The numerator is a quadratic equation with a x-intercept at x+2. The denominator is a cubic function. There must be one removable discontinuity at x=3, and there must be 2 infinite discontinuities at x= -1 and x= 2. How would I make this equation, please help!
Thanks!
Jacob
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Create an equation where: The numerator is a quadratic equation with a x-intercept at x+2. The denominator is a cubic function. There must be one removable discontinuity at x=3, and there must be 2 infinite discontinuities
at x = -1 and x = 2.
Note: You cannot have an x-intercept at x+2.
What did you mean to say?
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If you meant "x-intercept at x=2, the numerator must have a factor of (x-2)
but that means you have a removable discontinuity at x = 2.
So, where is the x-intercept?
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Removable discontinuity at x = 3 means
(x-3) must be a factor of numerator and denominator
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Infinite discontinuities at x = -1 and x = 2 means
(x+1) and (x-2) must be factors of the denominator
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f(x) = [(x-?)(x-3)]/[(x+1)(x-2)(x-3)]
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Cheers,
Stan H.
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