Which of the following lines does not intersect the graph of the function \(f(x)=\frac{1}{x}\)?

Correct answer: \(x=0\)

For \(f(x)=\frac{1}{x}\), the value at \(x=0\) is undefined, so the graph has no point on the line \(x=0\). Thus, \(x=0\) is the vertical asymptote and the graph does not intersect it. For comparison, with \(y=x\), the equation \(\frac{1}{x}=x\) gives \(x=\pm1\), so that line does intersect the graph. Exam tip: For \(y=\frac{1}{x}\), the asymptotes are \(x=0\) and \(y=0\).