1. Since the function is a natural log, any number can go inside the parenthesis besides zero and negative numbers therefore, the domain is (-infinity,1).
2. The range will be all the possible values of f(x). One way you can calculate the range is by analyzing the limit as x approaches negative infinity. When you do this, you realize that the function increases to infinity. We can also analyze the limit as x approaches 1. We realize that the function infinitely decreases. We can now conclude that the range is (-infinity,infinity).
3. For the asymptote, you look at where the function doesn't exist. You can find it by simply setting the insides of the parenthesis equal to zero. The asymptote of the function is therefore x=1.
4. For the intercepts, you set f(x)=0.
5. ln(1 -x) = 0
6. e^(ln(1-x)) = e^0
7. 1-x=1
8. x = 0
9. The intercept is 0.
2. The range will be all the possible values of f(x). One way you can calculate the range is by analyzing the limit as x approaches negative infinity. When you do this, you realize that the function increases to infinity. We can also analyze the limit as x approaches 1. We realize that the function infinitely decreases. We can now conclude that the range is (-infinity,infinity).
3. For the asymptote, you look at where the function doesn't exist. You can find it by simply setting the insides of the parenthesis equal to zero. The asymptote of the function is therefore x=1.
4. For the intercepts, you set f(x)=0.
5. ln(1 -x) = 0
6. e^(ln(1-x)) = e^0
7. 1-x=1
8. x = 0
9. The intercept is 0.