https://file.aiquickdraw.com/mathbot/file/17260078576837x843nhn.jpg

The given graph shows a transformation of the function \( f(x) = |x| \). The original absolute value function has its vertex at \( (0, 0) \) and opens upward with a slope of 1 on both sides.

### Analyzing the Transformation:
From the graph, we observe the following:
1. **Vertex Shift**: The vertex of the new function \( g(x) \) is located at \( (-2, 0) \), indicating a horizontal shift to the left by 2 units.
2. **Vertical Stretch**: The graph opens upward and appears narrower than the basic absolute value function, indicating a vertical stretch. The slope of the right side of the V is 2 instead of 1, so the function has been vertically stretched by a factor of 2.

### Writing the Transformation:
The general form of the transformation for an absolute value function is:
\[
g(x) = a |x - h| + k
\]
Where:
- \( a \) is the vertical stretch or compression factor.
- \( h \) represents the horizontal shift (right or left).
- \( k \) represents the vertical shift (up or down).

In this case:
-

The graph shows g(x), which is a transformation of f(x) = |x|. Write the function rule for g(x).

This problem explores the transformation of the absolute value function f(x) = |x|. The graph shows a horizontal shift by 2 units to the left and a vertical stretch by a factor of 2. Learn how to express the function g(x) in the form a|x - h| + k, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation