Question

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

f (x) = StartFraction x minus 5 Over 3 x squared minus 17 x minus 28 EndFraction
There are holes at x = 7 and x = negative four-thirds.
There are asymptotes at x = 7 and x = negative four-thirds.
There are asymptotes at x = –7 and x = four-thirds.
There are holes at (–7, 0) and x = four-thirds.

Answer 1

Correct statement: "There are asymptotes at x = 7 and x = −4/3."

Reason: 3x^2 − 17x − 28 = (3x + 4)(x − 7), so the denominator is zero at x = 7 and x = −4/3. The numerator x − 5 does not cancel either factor, so the discontinuities are nonremovable vertical asymptotes (not holes).