The question asks how to transform the graph of $y = 3^x$ to become the graph of $y = 3^{x-4} + 2$. Let me break this down step by step:

1. Horizontal Shift:

   • The term $x-4$ in $y = 3^{x-4} + 2$ shifts the graph of $y = 3^x$ 4 units to the right.

2. Vertical Shift:

   • The $+2$ outside the exponent causes a vertical shift, moving the graph 2 units up.

Transformation Instructions:

• Start with the graph of $y = 3^x$.
• Shift the graph 4 units to the right.
• Then, shift the resulting graph 2 units up.

Would you like more details or examples to clarify? Let me know!

Here are five related questions to expand your understanding:

1. What happens to the graph of $y = 3^x$ if the equation becomes $y = 3^{x+3} - 1$?
2. How do horizontal and vertical shifts affect the asymptote of an exponential function?
3. How do you determine the direction of a shift from the equation of a function?
4. How do transformations like $y = 3^{-x}$ and $y = 3^{x} + 5$ combine multiple effects?
5. What are the graphical differences between $y = 3^x$ and $y = 2^x$?

Tip: Remember, transformations do not change the shape of the graph, just its position!