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.

The given function \( g(x) \) has a y-intercept at \( (0, 5) \), meaning that when \( x = 0 \), \( g(0) = 5 \).

Now, consider the transformed function \( g(12x) \). To find the y-intercept of this new function, we substitute \( x = 0 \) into \( g(12x) \):

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

Since \( g(0) = 5 \) (from the original function's y-intercept), the y-intercept of \( g(12x) \) is also \( (0, 5) \).

Thus, the correct answer is:

**B. (0, 5)**

Would you like further details on how transformations affect the y-intercept? 

Here are five related questions to explore further:
1. How do horizontal stretches or compressions affect the graph of a function?
2. What effect does scaling by a factor of \( k \) inside the function argument \( f(kx) \) have on the graph?
3. How does the y-intercept of a function change with vertical shifts?
4. What is the difference between horizontal and vertical transformations?
5. Can a function have multiple y-intercepts?

**Tip:** Horizontal transformations like \( g(kx) \) only affect the x-values of the graph, leaving the y-values (like the y-intercept) unchanged.

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.

Explore how horizontal scaling affects the y-intercept of a function. This problem analyzes the effect of scaling on the function g(x) and provides a detailed solution, suitable for high school students. Learn how transformations such as g(kx) leave the y-intercept unchanged.

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