To solve this problem, you need to evaluate the function $f(x) = 4^x$ for the given values of $x$. Here's the step-by-step calculation:

Function: $f(x) = 4^x$

1. For $x = -2$: $f(-2) = 4^{-2} = \frac{1}{4^2} = \frac{1}{16}$

2. For $x = -1$: $f(-1) = 4^{-1} = \frac{1}{4}$

3. For $x = 0$: $f(0) = 4^0 = 1$

4. For $x = 1$: $f(1) = 4^1 = 4$

5. For $x = 2$: $f(2) = 4^2 = 16$

Completed Table:

Would you like me to explain this process further or assist with plotting the graph? Here are related questions for exploration:

1. What happens to $f(x) = 4^x$ as $x \to -\infty$?
2. How does the graph of $4^x$ compare to $2^x$?
3. What is the significance of the base of the exponential function in shaping the graph?
4. Can you describe the domain and range of $f(x) = 4^x$?
5. How do transformations (e.g., $f(x) = 4^x + 2$) affect the graph of $4^x$?

Tip: When graphing exponential functions, focus on understanding the behavior as $x \to \infty$ and $x \to -\infty$, as well as key points like the y-intercept.