4.5 Square Root and Cube Root Functions

Notes

• $\displaystyle y = \sqrt{x}$ starts at $(0, 0)$ and rises slowly to the right. Domain $x \ge 0$, range $y \ge 0$.
• $\displaystyle y = \sqrt[3]{x}$ passes through $(0, 0)$ and extends both ways. Domain and range are all real numbers.
• Transformations work the same as always: $\displaystyle y = a\sqrt{x - h} + k$ starts at $(h, k)$.
• If $a < 0$ the graph flips over, so the range becomes $y \le k$.
• Example: $\displaystyle y = \sqrt{x + 1} - 3$ starts at $(-1, -3)$ with domain $x \ge -1$ and range $y \ge -3$.