https://file.aiquickdraw.com/mathbot/file/1726504367428nu4bw7we.jpg

The graph shows two functions, \( f(x) \) and \( g(x) \), with \( f(x) \) represented by the blue curve and \( g(x) \) by the red curve. The task is to identify the transformation that converts \( f(x) \) into \( g(x) \).

### Key Observations:
- \( g(x) \) is the red curve, which appears to be a horizontal shift of \( f(x) \) (blue curve) to the right by 2 units.

This suggests that the transformation applied to \( f(x) \) to obtain \( g(x) \) is a **horizontal shift to the right** by 2 units. A horizontal shift to the right corresponds to the transformation:

\[
g(x) = f(x - 2)
\]

Thus, the correct answer is:

\[
g(x) = f(x - 2)
\]

### Do you need further explanation or have any questions?

Here are 5 related questions to deepen your understanding:
1. What happens when you shift a graph horizontally to the left by 3 units?
2. How does a vertical shift differ from a horizontal shift in graph transformations?
3. What transformation does \( g(x) = f(2x) \) represent?
4. Can you describe how \( g(x) = f(x) + 2 \) transforms the graph of \( f(x) \)?
5. What is the effect of the transformation \( g(x) = f(x+1) \) on \( f(x) \)?

**Tip**: Horizontal transformations affect the input (x-values), while vertical transformations affect the output (y-values).

The graphs of f(x) and g(x) are shown. Which equation describes g(x) as a transformation of f(x)?

Analyze the graphs of f(x) and g(x) to identify the transformation that converts f(x) into g(x). This problem focuses on horizontal shifts of functions, specifically shifting f(x) to the right by 2 units.

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