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 that they are both correct?

Answer 1

@whpalmer4

Answer 2

@Darius25

Answer 3

Well, if you have a denominator that equals 0 at those values of x, the function is undefined there. A denominator that looked like (x+1)(x-2)(x-4) would be such a denominator.

Now, if you have a more complicated fraction that has a denominator with those terms and some others as well, and the same (x+1)(x-2)(x-4) appears in the numerator, you could simplify the fraction, canceling out those terms to get a fraction which appears to be defined at those values of x. However, it only appears to be defined there — the restrictions from the original fraction still apply. This is why it is important to find any restrictions on the variable before simplifying the fraction!