Question

Which statement is true about the discontinuities of the function f(x)?

Answer 1

Answer:

so in short, the answer is C

Answer 2

In order to find out where your holes and asymptotes are is to factor both the top and the bottom of that rational function.  The numerator factors to (x+2)(x-2) and the denominator factors to x(x+1)(x-2).  So since there is an (x-2) in both the numerator and denominator, that is called a removable discontinuity which we also know as a hole.  The other factors in the denominator, the x and the (x+1) are vertical asymptotes, or values of x that make the rational function undefined (you're NEVER allowed to have a 0 in the denominator of a fraction!).  So your correct choice is c.  The way you find the y coordinate for the hole is to plug in 2 for x and solve it for y.  No biggie.