- List all asymptotes of the graph `y=2-1/x`. (2 marks)
--- 3 WORK AREA LINES (style=lined) ---
- Hence, sketch the graph of `y=2-1/x`. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
Show Answers Only
i. `text{Vertical asymptote at}\ \ x=0`
`text{Horizontal asymptote at}\ \ y=2`
ii.
Show Worked Solution
i. `y=2-1/x`
`text{Vertical asymptote at}\ \ x=0`
`text{As}\ x->oo, \ 1/x -> 0\ \ => 2-1/x -> 2`
`text{Horizontal asymptote at}\ \ y=2`
ii.
\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \ & \ \ 1\ \ & \ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex}\ \ \ y\ \ \rule[-1ex]{0pt}{0pt} & \frac{5}{2} & 3 & ∞ & 1 & \frac{3}{2} \\
\hline
\end{array}