Question

ramon is graphing the function $f(x) = 3(4)^x$. he begins by plotting the initial value. which graph represents his initial step? (graph with coordinate plane and point (0, 3) marked)

Explanation:

Step 1: Recall the form of an exponential function

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial value (the value of the function when \( x = 0 \)) and \( b \) is the base.

Step 2: Find the initial value of \( f(x) = 3(4)^x \)

To find the initial value, we substitute \( x = 0 \) into the function. Using the property of exponents that any non - zero number to the power of 0 is 1, i.e., \( 4^0=1 \).
So, \( f(0)=3\times(4)^0 = 3\times1=3 \).
This means the initial value occurs at the point \( (0, 3) \). We then look at the given graphs (even though only one graph with the point \( (0, 3) \) is shown here) and identify the graph that has the point \( (0, 3) \) plotted, as this is the initial step of graphing the exponential function (plotting the initial value).

Answer:

The graph with the point \((0, 3)\) plotted (the one shown with the point \((0, 3)\) marked on the \(y\) - axis at \(x = 0\)) represents his initial step.