Question

What are the transformations of:
f(x)=-log(2-x)+3

Answer 1

Our parent function for log is log (x), so how does your function differ?

1) The leading negative sign. This reflects rhe function across the x-axis.

2) The (2 - x) inside the log function. Note that this is actually two transformations because 2 - x is equivalent to -x + 2. A negative sign inside the log function flips the function across the y-axis and a shift inside the log function shifts the function opposite of the sign direction. +2 therefore shifts the function LEFT 2 units.

3) The +3 outside the log function simply is a vertical shift in the direction of the sign, so up 3 units.