# Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range. f(x)=lnx and g⟨x)=−ln(2x)

Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.
$$\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}{g}⟨{x}{)}=−{\ln{{\left({2}{x}\right)}}}$$

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Macsen Nixon
See explanation for graph. Starting with the graph of f(x) the graph of g(x) is stretched vertically and reflected over the x-axis, The domain for f(x) and g(x) is {x|x > 0}. The range for f(x) and g(x) is all real numbers. ‘The vertical asymptote for f(x) and g(x) is x=0.