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AP Calculus AB/Unit 1: Limits and Continuity
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Interpreting Limits and Asymptotes

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The function kk has a vertical asymptote at x=−3x = -3 and a horizontal asymptote at y=7y = 7. Given that lim⁡x→−3+k(x)=+∞ \lim_{x \to -3^+} k(x) = +\infty and lim⁡x→−∞k(x)=7 \lim_{x \to -\infty} k(x) = 7 , which of the following statements must be true?

A

© lim⁡x→−3−k(x)=7 \lim_{x \to -3^-} k(x) = 7 and lim⁡x→+∞k(x)=−3 \lim_{x \to +\infty} k(x) = -3

B

(B) lim⁡x→−3−k(x)=−∞ \lim_{x \to -3^-} k(x) = -\infty

C

(D) lim⁡x→−∞k(x)=7 \lim_{x \to -\infty} k(x) = 7

D

(A) lim⁡x→−3−k(x)=+∞ \lim_{x \to -3^-} k(x) = +\infty and lim⁡x→+∞k(x)=7 \lim_{x \to +\infty} k(x) = 7

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