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

The absolute value function \( g(x) \) has a y-intercept at \( (0, 5) \), which means that \( g(0) = 5 \).

To determine the y-intercept of \( g(12x) \), evaluate \( g(12x) \) at \( x = 0 \):
\[
g(12(0)) = g(0).
\]
Since \( g(0) = 5 \), the y-intercept of \( g(12x) \) is also \( (0, 5) \).

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

Would you like more details or have any further questions?

Here are 5 related questions to deepen understanding:
1. How does horizontal stretching or compression affect the graph of a function?
2. What happens to the x-intercepts of \( g(x) \) when it is transformed to \( g(12x) \)?
3. How would the y-intercept change if the function was \( g(x) + 3 \)?
4. What is the effect of vertical scaling on the y-intercept of an absolute value function?
5. How does the graph of \( g(12x) \) compare to that of \( g(x) \)?

**Tip**: When transforming functions, horizontal changes (like \( g(12x) \)) affect the graph's width, but vertical properties, such as the y-intercept, remain unchanged.

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

Explore how to determine the y-intercept of a transformed absolute value function g(12x), where the original function g(x) has a y-intercept at (0, 5). Learn about the effect of horizontal compression/stretching on the graph of a function. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation