Step 1 :The function given is \(f(x) = x^{2}\). This is a simple quadratic function, where each y-coordinate is the square of its corresponding x-coordinate.
Step 2 :Given the x-coordinates, we can determine the y-coordinates by substituting the x-values into the function.
Step 3 :For \(x = -1\), \(f(-1) = (-1)^{2} = 1\).
Step 4 :For \(x = 0\), \(f(0) = (0)^{2} = 0\).
Step 5 :For \(x = 1\), \(f(1) = (1)^{2} = 1\).
Step 6 :So, the three points on the graph are (-1, 1), (0, 0), and (1, 1).
Step 7 :The completed table is: \begin{tabular}{c|c} $\mathrm{x}$ & $\mathrm{y}$ \\ \hline -1 & 1 \\ 0 & 0 \\ 1 & 1 \end{tabular}