To determine the initial step in graphing the function $f(x) = 3 \cdot 4^x$, we need to identify the initial value of the function. The initial value is the value of the function when $x = 0$.

Let's calculate it:

$f(0) = 3 \cdot 4^0$

Since $4^0 = 1$, this simplifies to:

$f(0) = 3 \cdot 1 = 3$

Therefore, the initial value of the function $f(x) = 3 \cdot 4^x$ is $3$.

The graph representing Ramon’s initial step would be the one that shows a point at $(0, 3)$ on the coordinate plane. This point represents the initial value of the function, which is the output when the input $x$ is zero.

Would you like further details or have any questions?

Here are some related questions to further explore this topic:

1. How does changing the base of the exponential function affect its graph?
2. What would the graph of $f(x) = 3 \cdot 4^x$ look like for negative values of $x$?
3. If the function was $f(x) = 2 \cdot 4^x$, what would be the initial value?
4. How does the coefficient (in this case, 3) affect the shape of the graph?
5. What is the effect of adding a constant term to the function, such as $f(x) = 3 \cdot 4^x + 2$?

Tip: When graphing exponential functions, always start by plotting the initial value (the point where $x = 0$) to get a reference point for the rest of the graph.