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 that they are both correct? Justify your reasoning

Question

anonymous · Answer

when will bella be correct?  when it is vertical?

loser66 · Answer

Your prof give you a very tough problem to solve. To answer this question, you must completely understand the material

anonymous · Answer

i understand rational functions and quadratics i just don't know which function

loser66 · Answer

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.

loser66 · Answer

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

loser66 · Answer

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

anonymous · Answer

ohhh so they can't both be correct

loser66 · Answer

I think so

anonymous · Answer

wow thanks i get it now. can you help me on 2 more?

loser66 · Answer

Not sure whether I can or not, just post. If it is not me, definitely someone else will help

anonymous · Answer

ok thank you

anonymous · Answer

for that problem. if i change the numerator to anything else, would the answers for the problem still be the same? @Loser66

anonymous · Answer

im trying to come up with my own equation and trying to work it out myself