The problem asks for the equation of a transformed graph based on the original graph $f(x) = |x|$. The graph appears to have undergone a series of transformations, including scaling and possible reflections.

From the uploaded image, we observe the following:

1. The original $f(x) = |x|$ graph has its vertex at the origin $(0, 0)$ and is symmetric about the y-axis.
2. In the transformed graph:
   • The vertex remains at the origin $(0, 0)$, indicating no horizontal or vertical shifts.
   • The slopes of the two arms of the "V" shape are different from the original $f(x) = |x|$. Specifically:
     • The right arm has a slope of 3.
     • The left arm has a slope of $-3$.

This transformation is a vertical stretch of the graph $f(x) = |x|$ by a factor of 3.

Final Answer:

The equation for the transformed graph is: $y = 3|x|.$

Would you like further clarification or additional steps broken down?

Related Questions:

1. What happens to the graph of $y = |x|$ if it is vertically compressed instead of stretched?
2. How do horizontal stretches and compressions affect the equation of $f(x) = |x|$?
3. Can you explain the role of reflections in transforming $f(x) = |x|$?
4. How would adding a constant $c$ to $|x|$ affect the graph's position?
5. What is the difference between horizontal and vertical shifts in absolute value graphs?

Tip:

When identifying transformations, always analyze the vertex, slopes, and symmetry of the graph to match the transformations applied to the original equation.