Question 199693
An {{{asymptote }}}is a curve that{{{ y(x)}}} approaches, but {{{does}}}{{{ not}}}{{{cross}}}, as either {{{y }}}or {{{x}}} goes to {{{infinity}}}.



Your{{{ f(x)}}} has {{{no}}}{{{ asymptote}}}. The function{{{ f(x)}}} is identically equal to the line {{{f(x) = 4x}}} everywhere.



Your {{{g(x)}}}{{{ has}}} an asymptote at {{{x=0,}}} because {{{log(5x)}}} goes to {{{infinity}}} as {{{x}}} goes to {{{zero}}}. The graph of {{{g(x) }}}does{{{ not}}} cross the line {{{x=0}}}, but approaches it as closely as you might like.