The question asks us to analyze the transformation of the function $f(x) = -2x + 3$ when it is rotated counterclockwise, and then determine which among the given equations is a possible transformed function $g(x)$.

Key Idea:

When a function is rotated counterclockwise around the origin by 90 degrees, the slope of the line changes as follows:

• The slope $m$ of the original line becomes $-\frac{1}{m}$ in the transformed function.
• The intercept will also shift accordingly, but the primary concern here is the slope.

Original Function:

$f(x) = -2x + 3$

• Slope $m = -2$.

Transformed Slope:

The slope becomes: $m' = -\frac{1}{-2} = \frac{1}{2}.$

Thus, the transformed function will have a slope of $\frac{1}{2}$. We now match this with the provided options, considering the slopes.

Given Options:

1. $g(x) = x - 3$ (Slope = 1)
2. $g(x) = -4x + 3$ (Slope = -4)
3. $g(x) = -x + 3$ (Slope = -1)
4. $g(x) = 3x - 2$ (Slope = 3)

None of these options match the expected slope $\frac{1}{2}$. This suggests the provided choices might be missing the correct transformed function. Could you confirm if the choices are complete or provide additional information?

Let me know if you'd like further explanation or a deeper dive into related transformations.