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When looking at a rational function, Bella and Edward have two different thoughts. Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Describe a situation where Bella is correct, and describe a situation where Edward is correct. Is it possible for a situation to exist where they are both correct? Justify your reasoning

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- katieb

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- anonymous

ok, I give you the simplest form
to Bella, she said the functions is defined at x = -1, x =2 and x =4, her function should be
\[f(x) = \frac{x^2-6x+8}{(x^2+1)(x-2)(x-4)} \]
because when we factor the numerator, it cancel the last 2 terms of denominator and it turns to \[f(x)=\dfrac{1}{x^2+1} \] which is defined in all real number.

- anonymous

to Edward, just let the numerator =1, and (x-1) instead of (x^2-1) in denominator, the function turns to undefined at those points

- anonymous

They cannot be correct at the same time. That's what I thought

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