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).