Answer to Question #186362 in Functional Analysis for Catherine

Question

Which of the following rational functions does not have a vertical asymptote?

A. g(x) = 2x+7/x+5

B. h(x) = 2x²+7/3x²-5

C. k(x) = 2x² - 7/3x-5

D. f(x) = 2/ x²+5

Answer 1

A. Vertical asymptote $x=-5$

B. Vertical asymptotes $x=-\sqrt{5/3}$ and $x=\sqrt{5/3}$

C. Vertical asymptote $x=5/3$

D. There is no vertical asymptote.

Answer: D. $f(x)=2/(x^2+5)$