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.

Hello!

a rational function is undefined when has a denominator equal to zero, if we have the points x = -3, x = -4 and x= 6, Angie is right when the function has the form of where g(x) is a function defined in all the domain.

Then Jamal is correct when f(x) = g(x)/a(x) (because we already know that g(x) is defined in all the domain) where a(x) is not 0 in the points x = -3, x= -4 and x= 6 (for example take a(x) = 3x, that is only 0 when x =0).

there can't be a case where a function is undefined and defined at one point, then both of them can't be correct.

You could think in the next function:

in this case, when x = -3 both denominator and numerator are equal to zero, then you could think that this function is undefined at the point x= -3

but we can factorize the numerator as:

then this function, that early looked like undefined at x = -3, is actually defined at that point.