Is the function True or False

Question

Which of the following is true for  ?

Question options:

1)	There is a removable discontinuity at x = 3.
2)	There is a non-removable discontinuity at x = 3.
3)	The function is continuous for all real numbers.

Answer 1

Statement 1 is true. When you graph the function, you will see a hole in it at x = 3. That is manifest algebraically from the fact that the numerator factors into (x + 3)(x - 3) and the "x - 3" in the numerator cancels with the "x - 3" in the denominator. resulting in an "equivalent" function f(x) = x + 3 (except that this modified function does not result in a hole in the function at x = 3).