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?

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?

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