To determine which function $g(x)$ represents a translation of 7 units to the right and a reflection over the $x$-axis of the graph of $f(x) = \sqrt{x}$, let's break it down step by step:

1. Translation by 7 units to the right:
   A horizontal translation by 7 units to the right is represented by replacing $x$ with $x - 7$ in the function.
   So, starting with $f(x) = \sqrt{x}$, the function becomes: $f(x - 7) = \sqrt{x - 7}$

2. Reflection over the $x$-axis:
   Reflecting a function over the $x$-axis means multiplying the entire function by $-1$.
   So, reflecting $\sqrt{x - 7}$ over the $x$-axis gives: $g(x) = -\sqrt{x - 7}$

Therefore, the function that represents a translation of 7 units to the right and a reflection over the $x$-axis is: $g(x) = -\sqrt{x - 7}$

Let me know if you want further details or have any questions.

Here are 5 related questions for practice:

1. How would you modify $f(x) = \sqrt{x}$ for a translation 5 units to the left and a vertical stretch by a factor of 3?
2. What is the effect of reflecting the graph of $f(x) = x^2$ over the y-axis?
3. How does translating $f(x) = \sin(x)$ by 2 units up and 3 units to the right change the function?
4. What is the result of translating the function $f(x) = |x|$ by 7 units to the left?
5. What is the new equation after reflecting $f(x) = \ln(x)$ over the x-axis?

Tip: Translations along the x-axis are always done inside the function (replacing $x$ with $x - c$), while translations along the y-axis are done outside the function (adding or subtracting constants directly).