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.