What is the domain of g?
all real numbers
What is the x-intercept of g?
Where are the vertical asymptotes of g?
no vertical asymptote
Because ln(1-x) is defined only if 1-x>0, this means that x<1 for the function to be defined. The domain is (-∞, 1).
The x-intercept of g is when g(x)=ln(1-x)=0. Converted into exponential form, this is e0=1-x.
→x=0. The x-intercept of g is at (0, 0)
The vertical asymptote of g occurs when the inside of the parentheses in the ln function hits 0. In this case, our function is g(x)=ln(1-x).
1-x=0 → at x=1, there is a vertical asymptote because the domain is restricted x<1, and as x approaches 1 from the left, f(x) approaches -∞.