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 \( (0, 5) \), we can analyze what happens when the function becomes \( g(12x) \).

### Key steps to understanding:
1. **Definition of the \( y \)-intercept**: The \( y \)-intercept occurs where \( x = 0 \). For the function \( g(12x) \), we substitute \( x = 0 \) into \( 12x \) to find the corresponding \( y \)-value.
   
2. **Substitute \( x = 0 \) into \( g(12x) \)**: 
   \[
   g(12(0)) = g(0)
   \]
   From the given information, \( g(0) = 5 \). Hence, the \( y \)-intercept of \( g(12x) \) is \( (0, 5) \).

Thus, the \( y \)-intercept of \( g(12x) \) is the same as that of \( g(x) \), which is \( (0, 5) \).

### The correct answer is:
**B. (0, 5)**

Would you like more details or have any questions? Here are 5 related questions:

1. What happens to the graph of \( g(x) \) when it is transformed into \( g(kx) \)?
2. How do horizontal compressions and stretches affect the \( y \)-intercept of a function?
3. What is the effect of vertical shifts on the \( y \)-intercept of a function?
4. If \( g(x) \) has a \( y \)-intercept at \( (0, 5) \), what would happen if we transformed it to \( g(x) + 3 \)?
5. How does the absolute value function affect the symmetry of a function?

**Tip**: When transforming functions, remember that horizontal compressions or stretches affect the input (x-values), but they don’t change the \( y \)-intercept if you evaluate at \( x = 0 \).

If the absolute value 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.

Discover how the y-intercept of a transformed function is affected. Given that g(x) has a y-intercept at (0, 5), this problem explores how horizontal compression or stretching impacts the y-intercept of g(12x). Suitable for students in Grades 9-12.

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