Question

Use graphs and tables to find the limit and identify any vertical asymptotes of

Answer 1

first of all y=1/x looks like

and the vertical asymptote here is x=0
and you notice as we approach x=0 from left the y values approach -infinity
so we say
\[\lim_{x \rightarrow 0^-}f(x)=-\infty\]
and you notice as we approach x=0 from right the y values approach +infinity
so we say
\[lim_{x \rightarrow 0^+}f(x)=\infty\]

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so looking at y=1/(x-6)
means we are looking at just about the same graph with exception we are moving the vertical asymptote 6 units to the right