The function given is $f(x) = 8 \cdot 3^x$. Here's how we calculate $f(x)$ for $x = 0, 1, 2$ and graph the function:

1. Calculate $f(x)$ for each value of $x$:

   • For $x = 0$: $f(0) = 8 \cdot 3^0 = 8 \cdot 1 = 8$

   • For $x = 1$: $f(1) = 8 \cdot 3^1 = 8 \cdot 3 = 24$

   • For $x = 2$: $f(2) = 8 \cdot 3^2 = 8 \cdot 9 = 72$

2. Fill in the table:

   $x$	$f(x)$
   0	8
   1	24
   2	72

3. Graph the points $(0, 8)$, $(1, 24)$, and $(2, 72)$:

   • Mark these points on the provided graph grid.
   • Since the function $f(x)$ is exponential, connect the points smoothly in an upward curve as $x$ increases.

Let me know if you'd like a step-by-step guide for plotting or further details on exponential graphs!

Here are 5 related questions for you to explore:

1. What happens to $f(x)$ as $x$ becomes negative?
2. How does the base of the exponential, $3$, affect the growth rate?
3. What would the graph look like if the equation were $f(x) = 8 \cdot 2^x$?
4. What is the domain and range of $f(x)$?
5. Can you explain how the multiplier $8$ changes the graph compared to $f(x) = 3^x$?

Tip: Exponential functions grow faster as the base increases, so understanding base effects can help predict graph behavior!