Given the absolute value function $g(x)$ with a y-intercept at $(0, 5)$, this means that $g(0) = 5$.

Now, we need to determine the y-intercept of the function $g(12x)$. The y-intercept occurs where $x = 0$.

Step-by-Step Solution:

1. The y-intercept of $g(x)$ is found by evaluating $g(0)$, which gives $g(0) = 5$.
2. For $g(12x)$, substitute $x = 0$ into the function: $g(12(0)) = g(0)$ Since we already know that $g(0) = 5$, it follows that: $g(12(0)) = 5$ Thus, the y-intercept of $g(12x)$ is the same as the y-intercept of $g(x)$, which is at $(0, 5)$.

Conclusion:

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

Do you want further details or have any questions?

Here are 5 related questions:

1. What happens to the graph of $g(x)$ when it is transformed into $g(12x)$?
2. How do different transformations (like stretches and compressions) affect the y-intercept of a function?
3. Can you describe how to find the x-intercept of a transformed function?
4. What effect does multiplying the input by a factor have on the overall shape of the graph?
5. What are the key characteristics of an absolute value function?

Tip: When multiplying the input of a function by a constant, the y-intercept remains unchanged, as it depends on the value of the function when $x = 0$.