The question asks for the equation of the reflection of the function $f(x) = \frac{2x - 1}{x - 2}$, where $x \neq 2$, over the line $y = 3$.

Step-by-Step Solution:

1. Find the reflection formula: To reflect a function $f(x)$ across the line $y = c$, we use the formula: $y_{\text{new}} = 2c - f(x)$ where $c$ is the value of the line over which we are reflecting, and in this case, $c = 3$.

2. Apply the reflection: The function is reflected across $y = 3$, so: $y_{\text{new}} = 2(3) - f(x)$ $y_{\text{new}} = 6 - \left( \frac{2x - 1}{x - 2} \right)$

3. Simplify the expression: Subtract $f(x)$ from 6: $y_{\text{new}} = 6 - \frac{2x - 1}{x - 2}$ To simplify further, we can rewrite this expression as: $y_{\text{new}} = \frac{6(x - 2) - (2x - 1)}{x - 2}$ Simplify the numerator: $6(x - 2) = 6x - 12$ So: $y_{\text{new}} = \frac{6x - 12 - (2x - 1)}{x - 2}$ $y_{\text{new}} = \frac{6x - 12 - 2x + 1}{x - 2}$ $y_{\text{new}} = \frac{4x - 11}{x - 2}$

Thus, the equation of the reflected function is: $y = \frac{4x - 11}{x - 2}$

Would you like more details or have any other questions? Here are some related problems to expand your understanding:

1. How do you reflect a function over lines other than $y = c$?
2. What happens when you reflect a function over the x-axis?
3. How would you solve this problem if the reflection were over a different line, such as $y = 1$?
4. How can you graph the original function and its reflection?
5. What is the domain and range of the original function and its reflection?

Tip: When reflecting functions over lines, visualize the change geometrically to better understand the effect on the graph.