Question

1.9.3 quiz: finding vertical asymptotes
question 6 of 10
for the function $f(x)=\frac{1}{x}$, which of these could be a value of $f(x)$ when $x$ is close to zero?
a. -0.01

Explanation:

Step1: Analyze function behavior near 0

For $f(x)=\frac{1}{x}$, as $x$ approaches 0 from the positive side, $f(x)$ approaches $+\infty$; as $x$ approaches 0 from the negative side, $f(x)$ approaches $-\infty$. Values close to 0 for $x$ result in very large magnitude positive/negative values of $f(x)$.

Step2: Evaluate the given option

The option A is -0.01, which is a small magnitude number. This cannot be the value of $f(x)$ when $x$ is close to 0. Since this is the only visible option, and the function produces extreme values near $x=0$, we infer that the correct answer (if other options exist with large magnitude) would be a large positive or negative number, but based on the provided option:

Answer:

A. -0.01 is not a valid value. The function $f(x)=\frac{1}{x}$ produces values with very large magnitude (positive or negative) when $x$ is close to 0.

Note: If other options (e.g., 100, -100) exist, those would be the correct choices, as they match the extreme behavior of the function near $x=0$.