Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

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.

Discover how to graph the exponential function f(x) = 3 * 4^x by understanding its initial step. Learn how to find and plot the initial value (0, 3) on the coordinate plane. Suitable for high school students studying exponential functions and graphing.

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