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For Limit of StartFraction x squared minus 4 x minus 12 Over x minus 2 EndFraction as x approaches 2 minus =

✔ infinity

and Limit of StartFraction x squared minus 4 x minus 12 Over x minus 2 EndFraction as x approaches 2 plus=

✔ negative infinity

. These limits indicate there is an asymptote of

.

For Limit of StartFraction x squared minus 4 x minus 12 Over x minus 2 EndFraction as x approaches 2 minus infinity and Limit of

Answer :

The given rational function, that is, (x² - 4 · x - 12) / (x-2), has no horizontal asymptotes but one vertical asymptotes at x = 2.

How to determine the asymptotes of a rational function

A rational function has a horizontal asymptote if and only if the limit exists for x tending to ±∞. Rational functions have a limit if and only if the grade of the denominator is equal to or greater than the grade of the numerator. A vertical asymptote exists for all values of x such that the denominator equals 0.

Based on these facts, we conclude that the given rational function has no horizontal asymptotes but one vertical asymptotes at x = 2.

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Answer:

x=2

Step-by-step explanation:

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