https://file.aiquickdraw.com/mathbot/file/17250605487749lfqjan5.jpg

The graph above is a transformation of the function, write a formula for the function above

Let's analyze the transformation of the graph based on the original function \( f(x) = |x| \).

### Analysis of the Graph:

1. **Original Function**: The function \( f(x) = |x| \) is a V-shaped graph with its vertex at the origin (0, 0).

2. **Observations from the Graph**:
   - The vertex of the graph in the image is at \( (0, 3) \), not at the origin.
   - The slope of the right side of the graph (for \( x > 0 \)) is \(-1\), and the slope of the left side (for \( x < 0 \)) is \(1\).

### Determining the Transformation:

The graph appears to have been translated **up** by 3 units. Additionally, there is no horizontal or vertical stretch because the slopes remain at \( \pm 1 \).

### Equation for the Transformed Function:

Since the graph is shifted up by 3 units:
- **Vertical Translation**: We add 3 to the function.

Thus, the equation for the transformed function \( g(x) \) is:
\[
g(x) = -|x| + 3
\]

### Conclusion:

The equation for the function graphed above is \( g(x) = -|x| + 3 \).

Would you like more details or have any questions?

Here are some related questions to further explore:

1. How would the graph change if the function was \( g(x) = |x| - 3 \)?
2. What if the vertex of the graph was at \( (-2, 3) \)? What transformation would that represent?
3. How would a horizontal shift affect the equation of \( f(x) = |x| \)?
4. What would the equation look like if the graph was reflected over the x-axis after the translation?
5. How do you determine if a function has been horizontally stretched or compressed from a graph?

**Tip:** Always consider both horizontal and vertical changes when identifying transformations on graphs.

Explore the transformation analysis of the function g(x) = -|x| + 3 from its original form. Understand how graph translations affect the equation and graph characteristics. Suitable for high school students studying graph transformations in mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation