1. **State the problem:** We need to analyze and understand the function $f(x) = \sqrt{x} - 3$. 2. **Recall the domain of the square root function:** The expression inside the square root must be non-negative, so $x \geq 0$. 3. **Evaluate the function:** For any $x \geq 0$, $f(x) = \sqrt{x} - 3$. 4. **Find the intercepts:** - **y-intercept:** Evaluate $f(0) = \sqrt{0} - 3 = -3$. - **x-intercept:** Solve $f(x) = 0$: $$\sqrt{x} - 3 = 0$$ $$\sqrt{x} = 3$$ $$x = 3^2 = 9$$ 5. **Summary:** The function starts at $-3$ when $x=0$ and increases as $x$ increases, with the graph shifted down by 3 units compared to $y=\sqrt{x}$. **Final answer:** The function $f(x) = \sqrt{x} - 3$ has domain $x \geq 0$, y-intercept at $(0,-3)$, and x-intercept at $(9,0)$.