The absolute value function $g(x)$ has a y-intercept at $(0, 5)$. This means that $g(0) = 5$.

Now, we need to find the y-intercept of the transformed function $g(12x)$. The y-intercept of any function occurs where $x = 0$. So, we evaluate $g(12x)$ at $x = 0$:

$g(12(0)) = g(0) = 5$

Thus, the y-intercept of $g(12x)$ is still at $(0, 5)$.

Key Conclusion:

The y-intercept does not change under horizontal scaling (as in this case), so the y-intercept of $g(12x)$ remains at $(0, 5)$.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What effect does scaling by a factor inside the argument (e.g., $12x$) have on the graph of a function?
2. How does the y-intercept of an absolute value function change if there is a vertical shift?
3. What is the general form of a transformed absolute value function?
4. How would the x-intercept of $g(x)$ change when transforming to $g(12x)$?
5. What would happen to the y-intercept if we scaled vertically instead (e.g., $2g(x)$)?

Tip: When dealing with transformations of functions, horizontal scaling affects the graph's width but doesn't shift the y-intercept unless there is a vertical translation or reflection.