https://file.aiquickdraw.com/mathbot/file/17269969301271ux5r1sd.jpg

The image shows the following mathematical problem (translated from Indonesian):

- The function \( f(x) = 3^x + 4 \) is transformed into the graph of \( g(x) = 3^x + 6 \).
- The next part asks: "The function \( g(x) \) represents the translation of the function \( f(x) \) by..."

To solve this, we compare the two functions:
- \( f(x) = 3^x + 4 \)
- \( g(x) = 3^x + 6 \)

Both functions have the same base expression \( 3^x \), but \( g(x) \) has a constant value that is 2 units higher than \( f(x) \) (since \( 6 - 4 = 2 \)).

Thus, the function \( g(x) \) is the result of shifting the graph of \( f(x) \) vertically upwards by **2 units**.

Would you like a more detailed explanation or have any questions?

### Related Questions:
1. How do you determine horizontal shifts of functions?
2. What is the general formula for vertical shifts in function graphs?
3. How does adding or subtracting constants affect the graph of an exponential function?
4. Can this type of transformation be applied to other types of functions (like quadratic or linear)?
5. What would happen if the transformation was \( g(x) = 3^x + 2 \) instead?

### Tip:
To shift a graph vertically, you simply add or subtract a constant from the function's output. Adding shifts it up, while subtracting shifts it down.

Fungsi f(x) = 3^x + 4 menjadi grafik g(x) = 3^x + 6. Fungsi g(x) merupakan pergeseran fungsi f(x) sejauh...

Explore the transformation of the exponential function f(x) = 3^x + 4 to g(x) = 3^x + 6 by a vertical shift of 2 units. This problem is suitable for students in Grades 9-11, focusing on graph shifts and function transformations.

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