To analyze the effect of the composition $f(g(x))$ on the graph of $g(x)$, let's break down the functions and their composition:

Given functions:

• $f(x) = 4x$
• $g(x) = 2x$

Composition $f(g(x))$:

• First, apply $g(x)$ to $x$: $g(x) = 2x$
• Then, substitute $g(x)$ into $f(x)$: $f(g(x)) = f(2x) = 4(2x) = 8x$

Analysis:

• The function $f(g(x)) = 8x$ is a linear function with a slope of 8.
• The original function $g(x) = 2x$ has a slope of 2.

When comparing $g(x) = 2x$ to $f(g(x)) = 8x$, the slope has increased by a factor of 4 (from 2 to 8). This change in slope means that the graph of $g(x)$ is stretched vertically by a factor of 4 when transformed into $f(g(x))$.

Answer: B. $g(x)$ is stretched vertically.

Would you like more details on how function composition affects graphs or have any questions? Here are five related questions to consider:

1. What does it mean for a function to be stretched or compressed vertically?
2. How does horizontal stretching or compressing differ from vertical transformations?
3. What are the effects of different coefficients in linear functions on their graphs?
4. Can the composition of two functions result in both vertical and horizontal transformations? How?
5. What would be the effect on the graph if $f(x) = 4x + 1$ and $g(x) = 2x$?

Tip: When dealing with function compositions, focus on how the inner function modifies the input before applying the outer function to understand the overall transformation.