Question 116
What is the domain and the vertical asymptote (VA), respectively, of $$f(x) = \log_{5}(x-4)-4, x > 0$$?
Solution
For $$f(x) = \log_{5}(x-4)-4, x > 0$$ to be valid, (x-4) has to be greater than 0. Hence, x > 4
Now, the VA is a line that guides the graph (above which the graph is valid and below which it becomes invalid). Hence, it has to be the line x=4, as x>4 for the graph to be valid.
