Given the functions $f(x) = 4x$ and $g(x) = 2x$, let's analyze the composition $f(g(x))$ and determine its effect on the graph of $g(x)$.

Step 1: Find $f(g(x))$

• $g(x) = 2x$
• Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(2x) = 4 \times (2x) = 8x$

Step 2: Analyze the effect on the graph of $g(x)$

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

Comparing these slopes:

• The graph of $g(x)$ is stretched vertically by a factor of 4 because the slope increases from 2 to 8.

Thus, the correct answer is:

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

Would you like more details or have any other questions? Here are some related questions you might consider:

1. What happens to the graph of $g(x)$ if you compose it with a function that divides by 2?
2. How do horizontal stretches and compressions differ from vertical ones?
3. What is the effect of adding a constant to $f(x)$ before composing it with $g(x)$?
4. How would the composition change if $f(x)$ were a quadratic function?
5. What is the general effect of composing a linear function with another linear function?

Tip: Always pay attention to how the composition of functions affects the slope, as it directly influences the vertical stretch or compression.