The problem involves analyzing the transformation of the function $f(x) = x^2$ to the function $g(x) = (x - 4)^2$.

Step-by-Step Solution:

1. Transformation Analysis:

   • The function $g(x) = (x - 4)^2$ represents a horizontal translation of $f(x) = x^2$.
   • Specifically, the expression $(x - 4)$ indicates a shift 4 units to the right of the graph of $f(x)$.

2. Translation Direction:

   • Therefore, $g(x)$ is a translation of $f(x)$ by 4 units to the right.

3. Graph Identification:

   • Looking at the provided graphs:
     • In the correct graph, the red parabola (representing $g(x)$) should be shifted to the right of the blue parabola (representing $f(x)$).
     • In this case, the second graph on the right column correctly shows $g(x)$ translated 4 units to the right of $f(x)$.

Answer:

• The transformation is a horizontal shift 4 units to the right.
• The graph of $g(x)$ is correctly identified as the second one in the right column where the red parabola is to the right of the blue one.

Would you like further explanation on any specific step?

Here are 5 related questions for deeper understanding:

1. What would the transformation $g(x) = (x + 4)^2$ look like on the graph of $f(x) = x^2$?
2. How would you describe a vertical shift transformation for $f(x)$?
3. How does the function $g(x) = -x^2$ transform the graph of $f(x) = x^2$?
4. What effect does a horizontal compression have on the graph of $f(x)$?
5. How would the function $g(x) = (x - 4)^2 + 3$ affect the graph of $f(x) = x^2$?

Tip: For horizontal transformations, $(x - h)$ shifts the graph right by $h$ units, while $(x + h)$ shifts it left by $h$ units.