Calculus

If f is a continuous function with even symmetry and lim x→∞ f(x)=10, which of the following statements must be true?

I. lim x→∞ f(x)=10
II. there are no vertical asymptotes
III. The lines y=10 and y= -10 are horizontal asymptotes

a) I only
b) II only
c) I and II only
d) All statements are true

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  1. certainly (I), since that was given
    not (II) -- consider y=10 + 1/x
    not (III) since f(x) is even, so f(-x) = f(x)
    III is true if f(x) is odd.

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