The problem involves finding the correct transformation of the function $f(x)$ to obtain $g(x)$.

Analyzing the Graphs:

1. Original Function $f(x)$:

   • The orange curve represents $f(x)$.
   • This is a rational function with vertical and horizontal asymptotes at $x = 0$ and $y = 0$, respectively.

2. Transformed Function $g(x)$:

   • The blue curve represents $g(x)$.
   • Notice that $g(x)$ is a reflection of $f(x)$ about the x-axis, which implies a transformation of $f(x)$ to $-f(x)$.

3. Horizontal Translation:

   • The graph of $g(x)$ appears to be shifted to the right by 2 units when compared to $f(x)$.
   • A horizontal shift to the right is represented by replacing $x$ with $(x - 2)$ in the function.

Conclusion:

Given that $g(x)$ is obtained by reflecting $f(x)$ over the x-axis and then shifting it to the right by 2 units, the correct expression for $g(x)$ in terms of $f(x)$ is: $g(x) = -f(x - 2)$ However, it seems the incorrect answer was selected as $g(x) = -f(x) + 2$ on the provided options.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What effect does shifting a function to the left have on its equation?
2. How does reflecting a function over the y-axis change its equation?
3. If a function is reflected over the x-axis and then shifted up, how would its equation change?
4. How do horizontal shifts affect the domain of a function?
5. What transformations would you apply to obtain the equation $g(x) = f(-x + 3)$ from $f(x)$?

Tip: Always remember that a horizontal shift to the right is represented by subtracting from the $x$-value, while a shift to the left is represented by adding to the $x$-value.