Analyze \(y~=~\sqrt[3]{x~-~3}~+~2\). State \(a\), \(B\), \(h\), and \(k\); give the center, domain, and range; describe the transformation; and map parent anchors with inputs \(-8\), \(-1\), \(1\), and \(8\).
What this problem is really about
Cube roots differ from square roots because negative radicands are allowed, so preserve anchor points on both sides of the center. Read the transformation parameters, map symmetric perfect-cube inputs through the horizontal and vertical shifts, and trace the S-shaped curve through the translated center. Those two-sided anchors also make the all-real input and output behavior visible.