The graph of f(x)=4^x is transformed by a vertical reflection then a horizontal compression by a factor of 2, then a horizontal translation 3 units to the right, and finally a vertical translation of 5 units up. Question 5 (3 points) √ Saved What is the equation of the transformed function?

## Step 1: Vertical Reflection<br />### Reflecting the graph vertically involves multiplying the function by \(-1\). Thus, the function becomes \(f(x) = -4^x r\).<br />## Step 2: Horizontal Compression<br />### A horizontal compression by a factor of 2 is achieved by replacing \(x\) with \(2x\). The function becomes \(f(x) = -4^{2x} r\).<br />## Step 3: Horizontal Translation<br />### Translating the graph 3 units to the right involves replacing \(x\) with \(x-3\). The function becomes \(f(x) = -4^{2(x-3)} r\).<br />## Step 4: Vertical Translation<br />### Translating the graph 5 units up involves adding 5 to the function. The final transformed function is \(f(x) = -4^{2(x-3)} r + 5\).