1. **Problem Statement:** We are given a graph that represents a transformation of the exponential function $y=2^x$. The graph shows exponential decay, starting near $y=5$ at $x=-5$, passing through $y=1$ at $x=0$, and decreasing sharply below $y=-5$ by $x=3$. This suggests the function is reflected and translated downward. 2. **Recall the base function:** The original function is $y=2^x$, which is an exponential growth function with base 2. 3. **Reflection:** Reflection about the x-axis changes $y=2^x$ to $y=-2^x$. 4. **Vertical translation:** The graph passes through $y=1$ at $x=0$. For $y=-2^x + k$, when $x=0$, $y=-2^0 + k = -1 + k$. Since the graph passes through $y=1$ at $x=0$, we have: $$1 = -1 + k \implies k = 2$$ 5. **Final function:** The transformed function is: $$y = -2^x + 2$$ 6. **Explanation:** The negative sign reflects the graph over the x-axis, turning growth into decay. The $+2$ shifts the entire graph upward by 2 units, which aligns with the point $(0,1)$ on the graph. **Answer:** The equation of the transformed graph is: $$y = -2^x + 2$$