The question asks to determine which function represents the dotted graph given that the solid black graph is $y = f(x)$.

Analysis:

1. The dotted graph looks like a reflection of the solid black graph across the x-axis, which suggests a transformation involving a negative sign in front of the function: $y = -f(x)$.

2. Additionally, the dotted graph is shifted to the left, indicating a horizontal shift. Horizontal shifts are represented by modifications inside the function argument. Specifically, shifting left by 4 units corresponds to adding 4 inside the parentheses: $y = -f(x + 4)$.

Answer:

Thus, the correct function for the dotted graph is:

$y = -f(x + 4)$

Would you like a further breakdown of transformations, or help with another problem? Here are some related questions you might find useful:

1. What is the effect of a negative sign in front of a function on its graph?
2. How do horizontal shifts affect a function's graph?
3. How can you recognize reflections across the x-axis or y-axis?
4. What transformations occur with vertical shifts of a function?
5. How can you algebraically verify transformations in functions?

Tip: Remember that shifting $x$ to the left involves adding a positive number inside the parentheses: $f(x + a)$.