Question

6.9.3 quiz: finding vertical asymptotes
for the function ( f(x)=\frac{1}{x} ), which of these could be a value of ( f(x) ) when ( x ) is close to zero?

Explanation:

Step1: Analyze the function \( F(x)=\frac{1}{x} \)

When \( x\) approaches \( 0\) from the positive side (\(x
ightarrow0^{+}\)), \(F(x)=\frac{1}{x}\) approaches \(+\infty\). When \(x\) approaches \(0\) from the negative side (\(x
ightarrow0^{-}\)), \(F(x)=\frac{1}{x}\) approaches \(-\infty\).

Answer:

A very large positive or negative number (depending on the side from which \(x\) approaches \(0\)). For example, if \(x = 0.1\), \(F(x)=10\); if \(x=-0.1\), \(F(x)= - 10\). So values like \(100\), \(-100\) (any number with a large absolute value) could be values of \(F(x)\) when \(x\) is close to \(0\).