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.