https://file.aiquickdraw.com/mathbot/file/17270648477206sxgl096.jpg

The graph in the image shows two functions:

- \( f(x) = |x| \) in red, which is the absolute value function, forming a "V" shape.
- \( g(x) \) in blue, which looks like a vertical shift or transformation of \( f(x) \).

To identify \( g(x) \), observe how the blue graph differs from the red graph of \( f(x) \).

### Observations:
- The graph of \( g(x) \) seems to be vertically translated downward compared to \( f(x) \).
- Specifically, \( g(x) \) appears to be shifted by 2 units downward.

### Conclusion:
The transformation can be written as:
\[
g(x) = |x| - 2
\]
This is because shifting \( f(x) = |x| \) downward by 2 units modifies the graph accordingly.

Would you like more details or have any further questions? Here are five related questions for further practice:

1. What would happen if we shifted \( f(x) = |x| \) by 3 units upward instead of downward?
2. How do you reflect \( f(x) = |x| \) across the x-axis to form a new function?
3. What is the result of shifting \( f(x) = |x| \) 2 units to the right?
4. How would you describe the effect of multiplying \( f(x) = |x| \) by a constant greater than 1?
5. What happens when you apply a horizontal stretch to \( f(x) = |x| \)?

**Tip:** Always check for vertical or horizontal shifts when identifying transformations in functions.

The graph of f(x) = |x| is sketched in red and the graph of g(x) is sketched in blue. Use the translation rule and f(x) = |x| to identify the function g(x).

Learn how to identify the transformed function g(x) based on the absolute value function f(x) = |x|, involving a vertical shift. Explore key algebraic concepts of function transformations, including the vertical shifting theorem. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation