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 orvalues that the graph cannot take.
Ifthensince that would mean dividing by 0, andsinceThese equations can also be obtained from the formby considering the denominatorwhich may not take the value 0, soand the coefficient ofin numerator and denominator. LettinggivesIn fact ifthe equation of theasymptote is given by dividing the coefficient ofin numerator and denominator to give
Example:The equation of the x asymptote isand the equation of the asymptote is given bySketching the graph can be aiding by finding the intercepts with the axes.andThe graph is sketched below.