MathHelp please!

Question

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.

Answer 1

Edward is correct if the x values have factors located in the denominator.  When this happens, you have vertical asymptotes.

 

Bella is correct when the x values have factors located in the numerator ONLY.  When this happen, you have x-intercepts.

 

They are both correct when their factors are in both numerator and denominator.  When this happens, you have a hole.  This means the values are defined, but are also undefined.