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Draw the graph of y=|1-(1)/(|x|-2)|....

Draw the graph of `y=|1-(1)/(|x|-2)|`.

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We have `y=|1-(1)/(|x|-2)|`
Consider `y=(1)/(x-2)`, the graph of which is a rectangular hyperbola having centre at (2,0).

To draw the graph of `y=(1)/(|x|-2)`, in the above graph neglect the graph for `xlt0` and reflect the graph for `xge0` in the y-axis.

To draw the graph of `y=-(1)/(|x|-2)`, flip the above graph over the x-axis.

To draw graph `y=1-(1)/(|x|-2)`, shift the above graph 1 unit upward.

Hence the graph of `y=|1-(1)/(|x|-2)|` is as shown in the following figure.
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