Let's analyze the problem. You are asked to describe the transformations that convert the graph of $f(x) = 7^x$ to the graph of $g(x) = 7^{x-4}$.

Step 1: Understand the transformation

We can write $g(x) = 7^{x-4}$ as a transformation of $f(x)$. The function $g(x)$ is essentially the same exponential function as $f(x)$, but with a horizontal shift.

1. The function $g(x) = 7^{x-4}$ involves a horizontal shift. The term $x-4$ inside the exponent shifts the graph to the right by 4 units. This is because subtracting 4 from $x$ shifts the graph in the positive direction.

Step 2: Compare the transformations to the answer choices

Now we compare this horizontal shift to the provided choices:

• Option B: "The graph of $g$ is the graph of $f$ shifted $\boxed{4}$ units to the right."

This correctly describes the transformation. There is no stretching, reflection, or vertical movement involved. So, the correct answer is B.

Would you like any additional details on these transformations, or how they affect graphs?

Follow-up questions:

1. How would the graph change if the transformation was $g(x) = 7^{x+4}$?
2. What happens to the graph if we reflect $f(x) = 7^x$ over the x-axis?
3. Can you describe the effect of a vertical shift on an exponential graph like $f(x) = 7^x$?
4. What would a vertical stretch by a factor of 2 do to the graph of $f(x) = 7^x$?
5. How does changing the base (e.g., from 7 to 3) in an exponential function affect the graph?

Tip:

Always remember that a horizontal shift by $x - c$ moves the graph right by $c$ units, while $x + c$ shifts the graph left by $c$ units.