what happens as x approaches zero from the positive direction? f(x) gets larger. what happens as x…

Brief Explanations:

The problem asks about the behavior of a function $f(x)$ as $x$ approaches zero and the domain of the function. The provided information states that as $x$ approaches zero from the positive direction ($x \to 0^+$), $f(x)$ gets larger (approaches $+\infty$). As $x$ approaches zero from the negative direction ($x \to 0^-$), $f(x)$ gets larger in the negative direction (approaches $-\infty$). This behavior indicates that the function has a vertical asymptote at $x=0$. A vertical asymptote occurs where the function is undefined. The domain of a function consists of all input values ($x$) for which the function is defined. Since $f(x)$ is undefined at $x=0$, this value must be excluded from the domain. The tables show that the function is evaluated at both positive ($x=0.001, 0.01, 0.1, 1$) and negative ($x=-1, -0.1, -0.01, -0.001$) values of $x$. This suggests the function is defined for both positive and negative real numbers. Therefore, the domain includes all real numbers except for $x=0$.

Answer:

all real numbers x, except x = 0