Which statement is true about the discontinuities of the function f(x) = x-5/3x^2-17x-28 A)There are holes at x = 7 and .B)There are asymptotes at x = 7 and .C)There are asymptotes at x = –7 and .D)There are holes at (–7, 0) and .

1) function f(x)

              x - 5
f(x) = ----------------
          3x^2 - 17x - 28

2) factor the denominator:

3x^2 - 17x  - 28 = (3x + 4)(x - 7)

                        x - 5
=> f(x) = -----------------------
                (3x + 4) (x  - 7)

3) Find the limits when x → - 4/3 and when x → 7

Lim of f(x) when x → - 4/3 = +/- ∞

=> vertical assymptote x = - 4/3

Lim of f(x) when x → 7 = +/- ∞

=> vertical assymptote x = 7

Answer: there are assympotes at x = 7 and x = - 4/3