Question

For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?

Answer 1

The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:

$\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty$

What are the vertical asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:

$\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty$

More can be learned about vertical asymptotes at https://brainly.com/question/27949428

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