To solve the given problem:

We are tasked with writing the equation of a function whose graph is that of $y = \sqrt{x} + 3$, but reflected about the $x$-axis.

Step-by-Step Solution:

1. Understand Reflection Across the $x$-Axis:

   • Reflection across the $x$-axis means multiplying the entire function by $-1$.

2. Original Function: $y = \sqrt{x} + 3$

3. Apply the Reflection: Multiply the entire function by $-1$: $y = -(\sqrt{x} + 3)$

4. Simplify the Expression: Distribute the $-1$: $y = -\sqrt{x} - 3$

Final Answer:

$y = -\sqrt{x} - 3$

Let me know if you'd like additional explanations or examples! Here are some related questions for practice:

1. What is the effect of reflecting a function over the $y$-axis instead of the $x$-axis?
2. How would the graph of $y = \sqrt{x} - 3$ look after reflection across the $x$-axis?
3. What transformations occur when you add or subtract constants inside versus outside a square root function?
4. How would $y = \sqrt{x + 3}$ be reflected about the $x$-axis?
5. Can you describe the domain and range of the reflected function $y = -\sqrt{x} - 3$?

Tip: When reflecting functions, carefully observe whether the transformation impacts the function's range, domain, or symmetry properties.