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

To determine the y-intercept of $g(12x)$, evaluate $g(12x)$ at $x = 0$: $g(12(0)) = g(0).$ Since $g(0) = 5$, the y-intercept of $g(12x)$ is also $(0, 5)$.

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

Would you like more details or have any further questions?

Here are 5 related questions to deepen understanding:

1. How does horizontal stretching or compression affect the graph of a function?
2. What happens to the x-intercepts of $g(x)$ when it is transformed to $g(12x)$?
3. How would the y-intercept change if the function was $g(x) + 3$?
4. What is the effect of vertical scaling on the y-intercept of an absolute value function?
5. How does the graph of $g(12x)$ compare to that of $g(x)$?

Tip: When transforming functions, horizontal changes (like $g(12x)$) affect the graph's width, but vertical properties, such as the y-intercept, remain unchanged.