We are tasked with graphing the exponential function $f(x) = 3^x$ by creating a table of coordinates. To do this, substitute the given $x$-values into the function and compute the corresponding $y$-values.

Step-by-Step Calculation:

1. For $x = -2$: $f(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9}$

2. For $x = -1$: $f(-1) = 3^{-1} = \frac{1}{3}$

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

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

5. For $x = 2$: $f(2) = 3^2 = 9$

Completed Table:

Would you like me to graph this function or provide further analysis? Let me know!

Additional Questions:

1. Can you identify the domain and range of $f(x) = 3^x$?
2. How does the graph behave as $x \to -\infty$?
3. What is the y-intercept of the function $f(x) = 3^x$?
4. How does the base $3$ affect the growth of the function compared to a different base?
5. What happens to $f(x) = 3^x$ if it is transformed to $g(x) = 3^{x-1}$?

Tip:

Always check values of $x$ around 0 when graphing exponential functions to clearly observe their rapid growth or decay behavior.