To compare the graphs of $f(x) = 2x + 1$ and $g(x) = 2(x + 3) + 1$, let’s analyze the transformation applied to $f(x)$ to get $g(x)$.

1. Start with $g(x) = 2(x + 3) + 1$.
2. Distribute the 2 in $g(x)$: $g(x) = 2x + 6 + 1 = 2x + 7$

This gives us $g(x) = 2x + 7$.

Analyzing the Transformation

Comparing $f(x) = 2x + 1$ and $g(x) = 2x + 7$:

• The difference is in the constant term. $g(x)$ has a constant term of 7, while $f(x)$ has a constant term of 1.
• This means $g(x)$ is the graph of $f(x)$ translated 6 units up (since $7 - 1 = 6$).

However, upon rechecking, I realize that my answer needs to align with the options provided.

The correct answer from the options is not explicitly present, so I would need to check