To determine if the point with the x-coordinate of \(-\frac{2}{11}\) is located on the graph of the function \(f(x) = \frac{1}{x}\), we need to calculate \(f\left(-\frac{2}{11}\right)\).
Let's calculate this:
\[ f\left(-\frac{2}{11}\right) = \frac{1}{-\frac{2}{11}} = -\frac{11}{2} \]
This means that the function value at \(x = -\frac{2}{11}\) is \(-\frac{11}{2}\).
So, the point \(\left(-\frac{2}{11}, -\frac{11}{2}\right)\) is on the graph of the function \(f(x) = \frac{1}{x}\).
Therefore, the point with the x-coordinate of \(-\frac{2}{11}\) is \(\left(-\frac{2}{11}, -\frac{11}{2}\right)\).