If the absolute value child function g(x)
has a y
-intercept at  (0, 5)
, where is the y
-intercept of g(12x)
?

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).

If the absolute value child function g(x) has a y-intercept at (0, 5), where is the y-intercept of g(12x)?

Learn how to determine the y-intercept of a horizontally scaled function g(12x) when the original function g(x) has a y-intercept at (0, 5). This solution involves understanding function transformations, specifically horizontal scaling, and is suitable for students in Grades 9-10.

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