Answer:
The argument of the logarithmic function should be greater than zero.
Thus, for y = log(-x + 3) - 1 to be real-valued, we need:
-x + 3 > 0
or
x < 3
So, the domain of the function is all real numbers less than 3.
To find the range, let's consider the behavior of the logarithmic function.
As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.
As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.
Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.
Explanation: