Answer:
\(f(x)\) into the graph of \(g(x)\) without reflecting the graph across either axis.
Step-by-step explanation:
To transform the graph of \(f(x) = 4^x\) into the graph of \(g(x) = 4^{-x}\) without reflecting the graph across either axis, we need to follow these steps:
1. **Change the Exponent**:
- In \(f(x) = 4^x\), the exponent is x.
- In \(g(x) = 4^{-x}\), the exponent is -x.
- To transform \(f(x)\) into \(g(x)\), we need to change the exponent from x to -x.
2. **Effect of Changing the Exponent**:
- When the exponent changes from x to -x, the graph will be reflected over the y-axis.
3. **Graphing the Transformation**:
- Use a graphing tool or software to plot the graphs of both functions.
- The graph of \(f(x) = 4^x\) will show exponential growth.
- The graph of \(g(x) = 4^{-x}\) will show exponential decay due to the negative exponent.
By following these steps and observing the graphing tool, you can visually see the transformation of the graph of \(f(x)\) into the graph of \(g(x)\) without reflecting the graph across either axis.
