Key ideas

Square-root graphs:

• $y=\sqrt{x}$ is defined only for $x\ge 0$.
• Shifts: $y=\sqrt{x-a}+b$ shifts right by $a$ and up by $b$.
• A negative sign reflects the graph across the $x$-axis.

Cube-root graphs:

• $y=\sqrt[3]{x}$ is defined for all real $x$.
• Linear transformations like $y=k\sqrt[3]{x}+c$ stretch and shift the graph.