To create the equation for the function described, let's break it down step by step:

1. Original function: The original function is $f(x) = x$.
2. Shifted 8 units down: Shifting a function down by 8 units means subtracting 8 from the function. So, the new function becomes: $f(x) = x - 8$
3. Reflection in the x-axis: Reflecting a function over the x-axis means multiplying the entire function by $-1$. This transforms the function into: $f(x) = -(x - 8)$
4. Reflection in the y-axis: Reflecting the function over the y-axis means replacing $x$ with $-x$. So, we replace $x$ in the current function: $g(x) = -(-x - 8)$ Simplifying this expression: $g(x) = x + 8$

Thus, the equation of the new function is: $g(x) = x + 8$

Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does shifting a function up or down affect its graph?
2. What is the difference between reflecting a function over the x-axis and the y-axis?
3. Can you provide an example of a function reflected only over the y-axis?
4. How does combining transformations (shifts, reflections) affect the final function?
5. What is the impact of reflecting a quadratic function over both axes?

Tip: Always apply reflections carefully, and remember the order in which transformations are applied (reflections before shifts).