Question 116

What is the domain and the vertical asymptote (VA), respectively, of $$f(x) = \log_{5}(x-4)-4, x > 0$$?

Solution

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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.

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