The function $g(x)$ has a y-intercept at $(0, 5)$, which means $g(0) = 5$. Now, you're asked to find the y-intercept of the transformed function $g(12x)$.

Step-by-step solution:

1. Understanding the y-intercept:

   • The y-intercept of a function occurs where $x = 0$. So, to find the y-intercept of $g(12x)$, we substitute $x = 0$ into the transformed function.

2. Substitute into the transformed function:

   • $g(12x)$ becomes $g(12 \times 0) = g(0)$.

3. Use the given information:

   • We already know that $g(0) = 5$. So, the y-intercept of $g(12x)$ is also $(0, 5)$.

Conclusion:

The y-intercept of $g(12x)$ is $(0, 5)$, the same as the y-intercept of the original function.

Would you like further details or any clarifications?

Here are 5 related questions to explore:

1. How does horizontal scaling affect the x-intercept of a function?
2. What is the effect of vertical scaling on the y-intercept?
3. How do transformations like $g(12x)$ affect the slope of linear parts in a piecewise function?
4. How would a translation of the function $g(x)$ affect the y-intercept?
5. How do transformations affect the symmetry of an absolute value function?

Tip: Horizontal transformations involve changes to the input (x), while vertical transformations involve changes to the output (y).