Let . If the graph has vertical asymptotes at and a horizontal asymptote , what is ?
Answer and explanation
Correct answer: A.
- Step 1: Factor the numerator and denominator: and , so .
- Step 2: The factor cancels, creating a removable discontinuity at . The remaining zero of the denominator gives a single vertical asymptote at (). The horizontal asymptote is the ratio of leading coefficients: .
- Step 3: Sum the asymptote values: .
Answer
.
Why not the others: Other values confuse removable holes with non-removable vertical asymptotes, or include horizontal asymptote limits.
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