AP Calculus ABmediummcq1 pt
At which values of x does g(x) = (x + 2)/(x² - x - 6) fail to be continuous?
A.x = 3 only
B.x = -2 only
C.x = 3 and x = -2
D.No such values; g is continuous at every x
Explanation
Core Concept
Factoring gives x² - x - 6 = (x - 3)(x + 2), so the denominator vanishes at x = 3 and x = -2. At x = 3 the numerator equals 5, so g blows up and the discontinuity is infinite. At x = -2 the factor x + 2 cancels, leaving limit -1/5, a removable hole. Both points are discontinuities of g.
Correct Answer
Cx = 3 and x = -2
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