https://file.aiquickdraw.com/mathbot/file/1725368560000a3fqyii9.jpg

The text in the image is written in Indonesian and can be translated as follows:

"The function \( F(x) = 2^x \) is shifted 6 units to the right. The equation of the new function after the translation is:"

Given the information:

- The original function is \( F(x) = 2^x \).
- The function is shifted 6 units to the right.

To find the new function after a horizontal shift, we use the transformation rule for functions:

\[ F(x - h) \]

Where \( h \) is the horizontal shift. If the shift is to the right, \( h \) is positive. So, in this case, the new function \( G(x) \) after shifting \( F(x) = 2^x \) 6 units to the right is:

\[ G(x) = 2^{(x - 6)} \]

So, the equation of the new function is:

\[ G(x) = 2^{x-6} \]

Would you like more details on this or have any questions?

Here are some related questions:
1. What is the effect of shifting a function vertically versus horizontally?
2. How does the base of the exponential function affect its graph?
3. What happens to the graph of \( F(x) = 2^x \) if it is shifted to the left instead?
4. How would the function change if instead of shifting, it was reflected over the x-axis?
5. Can you generalize how to transform any function given different types of shifts and reflections?

**Tip:** When shifting functions horizontally, remember that moving to the right involves subtracting from the input variable, and moving to the left involves adding to it.

Fungsi F(x) = 2^x digeser 6 satuan ke kanan. Persamaan Fungsi baru setelah translasi adalah:

Explore how to translate the exponential function F(x) = 2^x by 6 units to the right. This problem delves into function transformations, providing a clear step-by-step guide suitable for high school students in Grades 9-12.

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