
.
The rational function
is defined over
, so is
.
We compute four limits:
It follows that the lines whose respective equations are
and
are asymptotes to the graph of
. Pay attention that the existence of the vertical asymptote is shown by the limit on the right at 2, but that on the left at 2 the function
has a finite limit.
As a composition of two differentiable functions,
is differentiable over
.
thus
all over
. It follows that
is a decreasing function on
and on
.
The graph and its asymptotes are displayed in Figure 5.
Figure:
The graph of
.
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Noah Dana-Picard
2007-12-28