https://file.aiquickdraw.com/mathbot/file/172593674177246m9rcix.jpg

To solve the transformation problem depicted in the image, let's analyze the given graph and the parent function.

### Step 1: Identify the Parent Function
The parent function appears to be \( y = |x| \), which is the absolute value function. This is indicated by the V-shaped graph.

### Step 2: Identify the Transformations
We need to determine how the parent function \( y = |x| \) is transformed into the red dashed graph.

- **Vertical Stretch/Compression**: Compare the slope of the lines. The parent function has a slope of \(1\) (or \(-1\) on the left side), but the red dashed graph has a slope of \(\frac{3}{2}\) (or \(-\frac{3}{2}\) on the left side). This indicates a vertical stretch by a factor of \(\frac{3}{2}\).
  
- **Horizontal Translation**: There is no horizontal shift, as the vertex remains at the origin \((0, 0)\).
  
- **Vertical Translation**: The red graph is shifted downward by 2 units, so a vertical translation of \(-2\) is applied.

### Step 3: Write the Transformation Equation
The transformed equation for the red graph, based on the transformations identified, is:

\[
g(x) = \frac{3}{2}f(x) - 2
\]

Substituting the parent function \( f(x) = |x| \):

\[
g(x) = \frac{3}{2}|x| - 2
\]

This equation should transform the parent function into the red dashed graph.

Would you like more details or have any questions about the solution?

### Further Questions:
1. How would the graph look if the parent function was \( y = x^2 \) instead of \( y = |x| \)?
2. What would happen if the graph were translated 3 units to the right?
3. How would the equation change if the graph were stretched horizontally instead of vertically?
4. What is the effect of changing the vertical translation from \(-2\) to \(+2\)?
5. How do you determine the vertex of the transformed graph?

### Tip:
When analyzing transformations, always start with identifying basic shifts (vertical/horizontal translations) before moving to stretches, compressions, or reflections.

What equation would transform the parent function y = f(x) into the new graph depicted in the image?

Learn how to transform the parent function y = |x| with a vertical stretch of 3/2 and a downward shift of 2 units. Understand how transformations such as stretching and translation affect the graph of an absolute value function. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation