Here are some functions that might (or might not) prove helpful when trying to complete the table. You could sketch each to see whether it has properties that you find useful. The functions are also available on cards to cut out.

\(y = (x-1)^2\)

\(y = x(1-x)\)

\(y = \dfrac{1}{\vert x \vert}\) for \(x \neq 0\)

\(y = 1 + \dfrac{1}{x}\) for \(x \neq 0\)

\(y = (x-1)^2 (x+3)\)

\(y = \dfrac{x-1}{x}\) for \(x \neq 0\)

\(y = x^3\)

\(y = \dfrac{x}{(x-1)^2}\) for \(x \neq 1\)

\(y = -1 + \dfrac{1}{x^2}\) for \(x \neq 0\)

\(y = \vert x \vert\)

\(y = x(x+7)\)

\(y = \dfrac{3}{x^2}\) for \(x \neq 0\)

\(y = x + \dfrac{1}{x}\) for \(x \neq 0\)

\(y = x^2 + 3\)

\(y = x\)

\(y = \dfrac{1}{x^3}\) for \(x \neq 0\)