Mathematics: Which description compares the vertical asymptotes of function a and function b correctly? function a- f(x) = 1/x-1 function b a. function a has a vertical asymptote at x =1 function b has a vertical asymptote at x =0 b. function a has a vertical asymptote at x = 1 function b has a vertical asymptote at x = -3 c. function a has a vertical asymptote at x = -1 function b has a vertical asymptote at x= -3 d. both functions have the same vertical asymptote.

Which description compares the vertical asymptotes

Ответ:

samanthaurso1

12.01.2022

Mathematics

Option B:

Function A has a vertical asymptote at x = 1

Function B has a vertical asymptote at x = -3

Step-by-step explanation:

A function f(x) has a vertical asymptote if:

$\lim_{x \to\\k^+}f(x) = \±\infty\\\\ \lim_{x \to\\k^-}f(x) = \±\infty$

This means that if there is a value k for which f(x) has infinity or a -infinity then x = k is a vertical asymptote of f(x). Therefore, the closer x to k approaches, the closer the function becomes to infinity.

We can calculate the asymptote for function A.

$\lim_{x \to \\1^+}(\frac{1}{x-1})\\\\ \lim_{x \to \\1^+}(\frac{1}{1^-1})\\\\ \lim_{x \to \\1^+}(\frac{1}{0}) = \infty\\\\and\\ \lim_{x \to \\1^-}(\frac{1}{x-1})\\\\\lim_{x \to \\1^-}(\frac{1}{0}) = -\infty$

Then, function A has a vertical asymptote at x = 1.

The asymptote of function B can be easily observed in the graph. Note that the function b is not defined for x = -3 and when x is closest to -3, f(x) approaches infinity.

Therefore x = -3 is asintota of function B.

Therefore the correct answer is option B.

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Ответ:

aljdones

14.05.2021

Mathematics

Step-by-step explanation:

I plugged each equation into a graphing calculator and compared them to see which one matched the one in the picture.

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