What are the transformations of:

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

To determine the transformations of the function f(x) = -log(2 - x) + 3, we need to break it down into its separate components.

First, let's focus on the log function. The general form of a logarithmic function is f(x) = log(base) (x). In our case, the base is not explicitly mentioned, so we assume it to be 10 (common logarithm).

The negative sign in front of the log function, f(x) = -log(2 - x), reflects the vertical reflection or a reflection across the x-axis. It means the function has been flipped vertically.

Next, let's look at the term (2 - x) inside the log function. This term represents the horizontal shift of the graph. Specifically, it shifts the graph of the parent logarithmic function f(x) = log(x) to the right by 2 units. The positive sign in front of (2 - x) indicates the rightward shift.

Finally, the constant term + 3 at the end of the function, f(x) = -log(2 - x) + 3, represents the vertical shift of the graph. It shifts the graph up by 3 units.

In summary, here are the transformations of the function f(x) = -log(2 - x) + 3:
1. Vertical reflection or reflection across the x-axis, indicated by the negative sign in front of the log function.
2. Rightward shift of 2 units, indicated by (2 - x) inside the log function.
3. Upward shift of 3 units, indicated by the constant term + 3 at the end of the function.