The question asks to identify which of the graphs correctly apply the transformations described.

Let’s analyze each option:

1. Option A: The transformation $f(x) \to f(x-2)$ represents a horizontal shift to the right by 2 units. The blue graph does show the red graph shifted right, so this transformation is correct.

2. Option B: The transformation $f(x) \to f(x+1)$ represents a horizontal shift to the left by 1 unit. However, the blue graph shifts right, not left, so this is incorrect.

3. Option C: The transformation $g(x) \to g(x-2)$ represents a horizontal shift to the right by 2 units. The blue graph matches this transformation since it is shifted right.

4. Option D: The transformation $f(x) \to f(x+1.5)$ represents a horizontal shift to the left by 1.5 units. The blue graph matches this transformation because the graph is shifted left.

Correct Answers: A, C, and D

Would you like a detailed explanation of the transformations or any clarifications?

Here are 5 related questions to enhance your understanding:

1. How does a transformation $f(x) \to f(x+c)$ affect the graph of $f(x)$?
2. What is the difference between horizontal and vertical shifts in transformations?
3. How do we recognize reflections in a graph?
4. What happens if we replace $x$ with $-x$ in $f(x)$?
5. Can multiple transformations (e.g., shifts and stretches) occur simultaneously?

Tip: Always check whether shifts are horizontal or vertical by looking at whether the transformation modifies $x$ (horizontal)