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The question is in Arabic and translates to:

> The equation \( y = -\left(\frac{1}{3}\right)^{x+5} \) represents the graph of the main function \( y = \left(\frac{1}{3}\right)^x \).

The goal seems to be to understand the relationship between the given function \( y = -\left(\frac{1}{3}\right)^{x+5} \) and the base function \( y = \left(\frac{1}{3}\right)^x \).

### Solution
1. **Transformation Analysis**:
   - **Original Function**: \( y = \left(\frac{1}{3}\right)^x \).
   - **Given Function**: \( y = -\left(\frac{1}{3}\right)^{x+5} \).

2. **Transformations Observed**:
   - **Horizontal Shift**: The exponent \( x+5 \) in the given function implies a **left shift** of 5 units. In general, \( y = \left(\frac{1}{3}\right)^{x+c} \) shifts the graph left if \( c \) is positive and right if \( c \) is negative.
   - **Reflection**: The negative sign in front of \( \left(\frac{1}{3}\right)^{x+5} \) indicates a reflection across the x-axis.

3. **Resulting Transformations**:
   - The base function \( y = \left(\frac{1}{3}\right)^x \) is shifted **5 units to the left** and then **reflected across the x-axis** to produce the given function \( y = -\left(\frac{1}{3}\right)^{x+5} \).

Would you like more details on any of these steps or have any further questions?

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### Additional Questions to Explore:
1. How does a horizontal shift affect the asymptote of the function?
2. What impact does a reflection over the x-axis have on the range of the function?
3. How would a vertical shift impact this function?
4. How does changing the base (e.g., from \( \frac{1}{3} \) to a different fraction) affect the function's behavior?
5. How would the graph change if we reflected it over the y-axis instead?

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**Tip:** When analyzing exponential functions, identify transformations systematically by examining shifts, reflections, and changes to the base separately.

المعادلة \( y = -\left(\frac{1}{3}\right)^{x+5} \) تمثل منحنى الدالة الرئيسية \( y = \left(\frac{1}{3}\right)^x \).

Understand the transformations applied to the exponential function y = (1/3)^x to produce y = -(1/3)^(x+5), including horizontal shift and reflection across the x-axis. Suitable for high school students studying function transformations.

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