The purpose of this investigation is to explore rational functions in the form of ??(??) ??(??) , where ??(??) and ??(??) were either linear or quadratic. The relationship between the rational functions and their asymptotic behaviour was also explored. In order to explore the this, graphs of four different types of rational functions, ??(??) = ???????????? ????????????, ??(??) = ???????????? ?????????????????? , ??(??) = ?????????????????? ???????????? and ??(??) = ?????????????????? ?????????????????? will be graphed using a graphing software Desmos. The investigation also focuses on three different asymptotes; vertical, horizontal and oblique. Vertical asymptotes (x=a) are vertical lines near which the function grows and approaches without bound. Horizontal asymptotes (y=c) are lines that the graph of the function approaches as the x value approaches positive or negative infinity. Oblique asymptotes are diagonal lines where the difference between the curve and line approach zero as the x value approaches positive and negative infinity. RECEIVED AN A-