Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.
Transform a fixed set of cube-root parent points
Problem
For \(y=\sqrt[3]{x}\), evaluate the parent inputs \(u=-8,-1,0,1,8\) and record each point \((u,\sqrt[3]{u})\). Identify the central point where \(u=0\) and confirm the odd symmetry of the point set.
Cube-root key points should include signed perfect cubes so both sides of the S-shaped graph are represented exactly. We’ll evaluate the fixed inputs, identify the central point, and pair opposite coordinates to verify rotational symmetry and the unrestricted real input and output sets.
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