1. **Problem:** Find the domain and range of the function $f(x) = \sqrt{x - 2}$ and create a table of values. 2. **Formula and rules:** The square root function $\sqrt{u}$ is defined only when $u \geq 0$. 3. **Domain:** Set the inside of the square root $x - 2 \geq 0$. $$x - 2 \geq 0$$ $$x \geq 2$$ So, the domain is all $x$ such that $x \geq 2$. 4. **Range:** Since the square root function outputs values $\geq 0$, and as $x$ increases, $\sqrt{x-2}$ increases, the range is $y \geq 0$. 5. **Table of values:** | $x$ | $f(x) = \sqrt{x - 2}$ | |-----|-----------------------| | 2 | $\sqrt{2-2} = 0$ | | 3 | $\sqrt{3-2} = 1$ | | 6 | $\sqrt{6-2} = 2$ | | 10 | $\sqrt{10-2} = \sqrt{8} \approx 2.83$ | 6. **Summary:** - Domain: $[2, \infty)$ - Range: $[0, \infty)$ The function starts at $x=2$ with $y=0$ and increases as $x$ increases.