https://file.aiquickdraw.com/mathbot/file/1726164129381nxunzqlr.jpg

The equation given is:

\[
y = -\frac{7}{4} |x|
\]

This equation is a transformation of the parent function \( f(x) = |x| \), which is the absolute value function. Let's break down the transformation and the graph:

### Step 1: Understanding the Transformation
The parent function \( f(x) = |x| \) is a V-shaped graph with a vertex at the origin \((0,0)\). Now, analyzing the given transformation:

1. **Vertical Stretch/Compression**:
   The coefficient \( -\frac{7}{4} \) affects the vertical stretch or compression. Since \( \frac{7}{4} > 1 \), this means the graph is **vertically stretched** by a factor of \( \frac{7}{4} \).

2. **Reflection**:
   The negative sign in front of the fraction indicates that the graph is reflected across the **x-axis**.

### Step 2: Choosing the Correct Graph
- The correct graph will show a V-shape with a steeper slope than the parent function due to the stretch and should be reflected across the x-axis (pointing downward).

Looking at the given options:
- **Graph C** appears to be the correct one** because it shows both the reflection and the vertical stretch.

### Step 3: Describing the Transformation
Based on the analysis:
- The correct statement describing the transformation is **C. The parent function is stretched vertically and reflected in the x-axis**.

### Conclusion:
- The correct graph is **C**.
- The correct transformation statement is **C**.

Would you like more details or clarifications? Here are five related questions to expand this concept:

1. How does a horizontal stretch or compression affect the graph of \( |x| \)?
2. What happens if the coefficient is less than 1 but greater than 0 (e.g., \( \frac{1}{2} |x| \))?
3. How do shifts (horizontal or vertical) affect the graph of an absolute value function?
4. How can you determine the vertex of a transformed absolute value function?
5. What would the graph look like if the function was \( y = \frac{7}{4} |x| \) instead?

**Tip:** Always analyze the transformation of a function by identifying whether it's a reflection, stretch, or shift, and whether it affects the horizontal or vertical direction.

Graph the equation and describe the transformation from the parent function f(x) = |x|. The equation is y = -7/4|x|.

Learn how to graph and describe the transformation of the absolute value function y = -7/4|x|. This covers key concepts such as vertical stretching, reflection across the x-axis, and transformations of the parent function f(x) = |x|. Suitable for students in Grades 9-11.

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