To determine which function represents the dotted graph, let's analyze the transformation applied to the solid graph of $y = |x|$, which is the absolute value function.

Analysis:

1. The solid black graph is the standard absolute value function $y = |x|$.
2. The dotted graph appears to be:
   • Reflected across the x-axis.
   • Shifted downward by 4 units.

These observations suggest the transformation follows: $y = -|x| - 4$

Correct Answer:

The function representing the dotted graph is $y = -|x| - 4$.

Do you want a step-by-step explanation or any further clarification? Here are some related questions you might want to explore:

1. What are transformations of the absolute value function?
2. How does reflection across the x-axis affect a graph?
3. What happens when a graph is shifted vertically?
4. Can you explain how $y = -|x| + 4$ would look compared to $y = |x|$?
5. How do you determine shifts in absolute value functions from their equations?

Tip: Reflections and vertical shifts are common in graph transformations—practice recognizing them visually!