https://file.aiquickdraw.com/mathbot/file/1730206229594ouq21c6e.jpg

The question in Arabic translates to:

"If \( \mathcal{G}(x) \) below represents the transformation of the graph of the main function \( y = \left(\frac{1}{2}\right)^x \), what is the equation of \( \mathcal{G}(x) \)?"

To solve this, we need to understand what transformations have been applied to the original function \( y = \left(\frac{1}{2}\right)^x \) to produce the function \( \mathcal{G}(x) \).

If there are any specific transformations described in the rest of the problem, let me know so I can provide a complete solution. Alternatively, please provide more details on what transformations are implied if the context is missing in the image. 

Would you like me to go over types of transformations typically applied to functions like these, or do you have any additional details? 

Here are 5 related questions to expand your understanding:

1. What is the effect of a horizontal shift on exponential functions?
2. How does a vertical shift impact the graph of \( y = \left(\frac{1}{2}\right)^x \)?
3. How does reflecting an exponential function affect its graph?
4. What happens to the graph of \( y = \left(\frac{1}{2}\right)^x \) when multiplied by a constant?
5. How can we determine the transformations of a function from its equation?

**Tip:** When dealing with exponential functions, pay close attention to whether transformations are inside (affecting \( x \)) or outside (affecting the entire function) to correctly interpret shifts, stretches, or reflections.

If \( \mathcal{G}(x) \) represents the transformation of the graph of the main function \( y = \left(\frac{1}{2}\right)^x \), what is the equation of \( \mathcal{G}(x) \)?

Explore how to determine the equation of \( \mathcal{G}(x) \), a transformation of the exponential function \( y = \left(\frac{1}{2}\right)^x \). Understand key concepts in graph transformations, including reflections, shifts, and stretches for exponential functions. Suitable for Grades 10-12.

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