1. **State the problem:** We are given the function $$f(x) = - \frac{5}{4} \left(\frac{4}{5}\right)^{x + 4} + 2$$ and need to analyze it. 2. **Identify the type of function:** This is an exponential function of the form $$f(x) = a \cdot b^{x + c} + d$$ where $$a = -\frac{5}{4}$$, $$b = \frac{4}{5}$$, $$c = 4$$, and $$d = 2$$. 3. **Classify growth or decay:** Since $$0 < b = \frac{4}{5} < 1$$, the function involves exponential decay. 4. **Explain the effect of parameters:** - The base $$b = \frac{4}{5}$$ is the decay factor. - The negative coefficient $$a = -\frac{5}{4}$$ reflects the graph over the x-axis and scales it. - The $$+2$$ shifts the graph vertically upward by 2 units. 5. **Graph function:** The function is $$f(x) = - \frac{5}{4} \left(\frac{4}{5}\right)^{x + 4} + 2$$. 6. **Summary:** - Exponential decay with decay factor $$\frac{4}{5}$$. - Reflected and shifted vertically. --- **Final answer:** - The function represents exponential decay with decay factor $$\frac{4}{5}$$.