To determine the equation of $g(x)$ from $f(x)$, let's analyze the transformations applied to the graph of $f(x)$ to obtain the graph of $g(x)$.

Given the image, $f(x)$ is a square root function, likely $f(x) = \sqrt{x}$. The graph of $g(x)$ is shifted upwards and possibly stretched.

Step-by-Step Analysis:

1. Identify the basic function $f(x)$: $f(x) = \sqrt{x}$ This corresponds to the black graph in the image.

2. Vertical shift: The blue graph $g(x)$ appears to be a vertical translation of $f(x)$. It has been shifted up by 4 units.

   Therefore, the equation for $g(x)$ based on this shift is: $g(x) = \sqrt{x} + 4$

Thus, the equation for $g(x)$ is: $g(x) = \sqrt{x} + 4$

Would you like more details on any specific part of this transformation process or have any further questions?

Related Questions:

1. What would be the equation if $g(x)$ was shifted 3 units down instead of up?
2. How does a horizontal shift affect the equation of a square root function?
3. What transformation occurs if $g(x) = 2\sqrt{x}$?
4. How do combined transformations (e.g., vertical shift and horizontal stretch) affect the function?
5. If $g(x) = \sqrt{x - 2} + 4$, what transformation does $-2$ represent?

Tip:

When identifying transformations, always consider how each parameter (vertical shift, horizontal shift, stretching, reflection) affects the function's graph.