To update a function $f(x)$ to reflect the specified transformations, we'll break them down step by step:

1. Vertical Stretch of 3: Multiply the function $f(x)$ by 3.
   $f(x) \to 3f(x)$.

2. Horizontal Stretch of 1: A horizontal stretch factor of 1 means no change to the horizontal scaling. The function remains the same in this respect.

3. Vertical Shift of 0: No vertical shift means there’s no added constant to the function. Again, no change here.

4. Horizontal Shift of 5: Shift the function 5 units to the right by replacing $x$ with $x - 5$.
   $f(x) \to f(x - 5)$.

5. Reflection over the x-axis: Multiply the entire function by $-1$ to reflect it.
   $f(x) \to -f(x)$.

Final Transformed Function

Combining all transformations, the updated function becomes:
$g(x) = -3f(x - 5)$

This means:

• The vertical stretch of 3 scales the height of the graph.
• The horizontal shift moves the graph 5 units to the right.
• The reflection flips it over the x-axis.

If the original function $f(x)$ is provided (e.g., $f(x) = x^2$), you can substitute it to determine the final expression for $g(x)$. Let me know if you’d like to proceed with a specific example.

---

Would you like me to clarify further, or apply this to a specific function?
Here are 5 related questions for practice:

1. What happens to the function if we change the vertical stretch to $\frac{1}{2}$?
2. How does a horizontal stretch of $\frac{1}{2}$ differ from a horizontal stretch of 2?
3. If the function is $f(x) = \sin(x)$, what does the transformed graph look like?
4. Can you reverse these transformations? What would the inverse function look like?
5. What is the effect of combining multiple transformations, such as vertical compression and a reflection?

Tip: Always apply shifts last when performing transformations, as they change the location of the function graph.