The equation g(x) = √(3x - 3) (first option) represents the transformation formed by horizontally stretching the graph of f(x) = √x by a factor of 3 and then vertically shifting the graph 3 units down. This is because horizontally stretching by a factor of a involves replacing x with x/a, and vertically shifting down b units involves subtracting b from the function.
The correct equation is g(x) = √(3x - 3).
Here's why:
Horizontal stretching by a factor of 3: When we stretch a graph horizontally by a factor of a, we replace each x-value in the original function with x/a. In this case, we want to stretch the graph by a factor of 3, so we replace x with x/3 in the function. This gives us f(x/3).
Vertical shift down 3 units: When we shift a graph vertically by b units, we add or subtract b to the entire function. Here, we want to shift the graph down 3 units, so we subtract 3 from the function. So, we have g(x/3) - 3.
Combining these transformations, we get the final equation: g(x) = √(3x - 3).