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lowcard2
When looking at a rational function, Jamal and Angie have two different thoughts. Jamal says that the function is defined at x = -3, x = -4, and x = 6. Angie says that the function is undefined at those x values. Describe a situation where Jamal is correct, and describe a situation where Angie is correct. Is it possible for a situation to exist that they are both correct? Justify your reasoning.
Hint for part of this: Think of a fraction. A fraction doesn't exist when its bottom is zero. like x+3 is zero when x=-3. The fraction 1/(x+3) does not exist at x=-3.
Angie is correct if this were the case\[\frac{ 1 }{ (x+3)(x+4)(x-6) }\] because if any of those values were put it in, the denominator would be zero. Can't divide by zero...now can we? Jamal would be correct if \[(x+3) +(x-4) + (x-6)\] Both could be correct if this were the case: \[\frac{ (x+3)(x+4)(x-6) }{ (x+3)(x+4)(x-6) }\] because even though the bottom is zero, so is the top. 0/0 is still zero. So..maybe we can divide by zero after all.