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

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 \( x = 0 \).

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

Find the y-intercept of the transformed absolute value function g(12x) when the original function g(x) has a y-intercept at (0, 5). This problem involves understanding function transformations and their effects on intercepts, suitable for students in Grades 9-10.

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