Asymptotes are equations that describe the behaviour of a curve as one coordinate tends to infinity. For reciprocal graphs – any graph of the form
– the asymptotes are the set of
– values or
values that the graph cannot take.
If
then
since that would mean dividing by 0, and
since
These equations can also be obtained from the form
by considering the denominator
which may not take the value 0, so
and the coefficient ofin numerator and denominator. Letting
gives
In fact if
the equation of theasymptote is given by dividing the coefficient ofin numerator and denominator to give
Example:
The equation of the x asymptote is
and the equation of the asymptote is given by
Sketching the graph can be aiding by finding the intercepts with the axes.
and
The graph is sketched below.
