Subjects algebra

Vertical Asymptote E4Fc74

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Vertical Asymptote E4Fc74


1. Let's start by understanding what a vertical asymptote is. 2. A vertical asymptote occurs in a function when the function approaches infinity or negative infinity as $x$ approaches a certain value. 3. Typically, vertical asymptotes happen where the denominator of a rational function is zero and the numerator is not zero at that point. 4. If $x = -5$ is not a vertical asymptote, it means that either the function is defined at $x = -5$ or the behavior near $x = -5$ does not tend to infinity. 5. For example, if the function is $f(x) = \frac{(x+5)(x-2)}{x+5}$, then at $x = -5$, the factor cancels out, and the function simplifies to $f(x) = x - 2$, which is defined and finite at $x = -5$. 6. Therefore, $x = -5$ is not a vertical asymptote because the function does not blow up to infinity there; instead, it has a removable discontinuity or is continuous. 7. To confirm, check the limit of the function as $x$ approaches $-5$. If the limit is finite, no vertical asymptote exists at $x = -5$. Final answer: $x = -5$ is not a vertical asymptote because the function does not approach infinity or negative infinity at that point; it is either defined or has a removable discontinuity there.