Find the domain and range of the function :
\Domain of the function is all possible values of .
Observe the graph of the function.
\The function is defined at all possible values of except
and
.
Thus, the domain is .
Range of the function is all possible values of .
Observe the graph of the function.
\Range of the function is .
Find intercepts, if any :
\Observe the graph of the function.
\The intercepts is .
Find horizontal asymptotes, if any :
\The line is a horizontal asymptote of the function
if
approaches
as
approaches
.
Observe the graph of the function.
\The horizontal asympote is .
Find vertical asymptotes, if any :
\The line is a vertical asymptote of the function
if
approaches
as
approaches
from the right or left.
Observe the graph of the function.
\The vertical asympotes are and
.
Find oblique asymptotes, if any :
\When a linear asymptote is not parallel to the - or
-axis, it is called an oblique asymptote (or) slant asymptote.
Observe the graph of the function.
\There is no oblique asympote.
\Domian : .
Range : .
Intercepts :
.
horizontal asymptotes :
.
Vertical asymptotes :
and
.
Oblique asymptotes : None.