Given that $g(x)$ has a $y$-intercept at $(0, 5)$, we can analyze what happens when the function becomes $g(12x)$.

Key steps to understanding:

1. Definition of the $y$-intercept: The $y$-intercept occurs where $x = 0$. For the function $g(12x)$, we substitute $x = 0$ into $12x$ to find the corresponding $y$-value.

2. Substitute $x = 0$ into $g(12x)$: $g(12(0)) = g(0)$ From the given information, $g(0) = 5$. Hence, the $y$-intercept of $g(12x)$ is $(0, 5)$.

Thus, the $y$-intercept of $g(12x)$ is the same as that of $g(x)$, which is $(0, 5)$.

The correct answer is:

B. (0, 5)

Would you like more details or have any questions? Here are 5 related questions:

1. What happens to the graph of $g(x)$ when it is transformed into $g(kx)$?
2. How do horizontal compressions and stretches affect the $y$-intercept of a function?
3. What is the effect of vertical shifts on the $y$-intercept of a function?
4. If $g(x)$ has a $y$-intercept at $(0, 5)$, what would happen if we transformed it to $g(x) + 3$?
5. How does the absolute value function affect the symmetry of a function?

Tip: When transforming functions, remember that horizontal compressions or stretches affect the input (x-values), but they don’t change the $y$-intercept if you evaluate at $x = 0$.