1. **State the problem:** We are given the equation $y + 3 = \sqrt{x}$ and want to understand its graph and behavior. 2. **Rewrite the equation:** To isolate $y$, subtract 3 from both sides: $$y + 3 = \sqrt{x} \implies y = \sqrt{x} - 3$$ 3. **Domain considerations:** Since $\sqrt{x}$ is defined only for $x \geq 0$, the domain of this function is $x \geq 0$. 4. **Graph behavior:** The graph of $y = \sqrt{x}$ starts at $(0,0)$ and increases slowly. Shifting it down by 3 units means the graph starts at $(0, -3)$. 5. **Check points:** - At $x=0$, $y = \sqrt{0} - 3 = 0 - 3 = -3$ - At $x=4$, $y = \sqrt{4} - 3 = 2 - 3 = -1$ 6. **Summary:** The graph is the standard square root curve shifted down by 3 units, defined only for $x \geq 0$. **Final answer:** $$y = \sqrt{x} - 3$$