Final answer:
The domain of the function f(x) = ln(2-x) is all real numbers except x = 2. The vertical asymptote is x = 2. The end behavior of the function is that as x approaches negative infinity, ln(2-x) approaches positive infinity, and as x approaches positive infinity, ln(2-x) approaches negative infinity.
Step-by-step explanation:
For the function f(x) = ln(2-x), the domain is the set of all real numbers except x = 2.
This is because the natural logarithm is only defined for positive real numbers, and since 2-x must be positive, x cannot be equal to 2.
The vertical asymptote is the line x = 2. As x gets arbitrarily close to 2 from either side, the value of ln(2-x) approaches negative infinity.
The end behavior of the function is as follows: as x approaches negative infinity, ln(2-x) approaches positive infinity, and as x approaches positive infinity, ln(2-x) approaches negative infinity.