If the absolute value child function g(x)
 has a y
-intercept at (0, 5)
, where is the y
-intercept of g(12x)
? 
A.(0, 2.5)

B.(0, 5)

C.(0, 10)

D.There is no y
-intercept.

Given that \( g(x) \) has a \( y \)-intercept at \( (0, 5) \), this means that:

\[
g(0) = 5
\]

Now, we are asked to find the \( y \)-intercept of \( g(12x) \). To find the \( y \)-intercept of a function, we set \( x = 0 \) in the function. So, for \( g(12x) \):

\[
g(12(0)) = g(0)
\]

Since we know \( g(0) = 5 \), it follows that:

\[
g(12(0)) = 5
\]

Thus, the \( y \)-intercept of \( g(12x) \) is also at \( (0, 5) \).

The correct answer is:

**B. (0, 5)**

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Do you need further details or have any other questions?

Here are five related questions:
1. What happens to the graph of \( g(x) \) when transformed to \( g(12x) \)?
2. How does a vertical stretch or compression affect the \( y \)-intercept of a function?
3. What would happen to the \( y \)-intercept if the function were \( g(x/2) \)?
4. How do horizontal transformations affect the shape of a graph?
5. Why is the \( y \)-intercept unchanged by horizontal compressions or stretches?

**Tip:** Horizontal transformations do not affect the \( y \)-intercept, as they only impact how the function behaves along the \( x \)-axis.

If the absolute value child function g(x) has a y-intercept at (0, 5), where is the y-intercept of g(12x)? A.(0, 2.5) B.(0, 5) C.(0, 10) D.There is no y-intercept.

Learn how to find the y-intercept of a transformed absolute value function g(12x) given the original y-intercept at (0, 5). Understand key concepts in function transformations, including horizontal stretches and compressions. Suitable for students in Grades 9-11.

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