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14 Pages Essays / Projects Year: Pre-2021

The purpose of this investigation is to explore rational functions in the form of 𝑓𝑓(π‘₯π‘₯) 𝑔𝑔(π‘₯π‘₯) , where 𝑓𝑓(π‘₯π‘₯) and 𝑔𝑔(π‘₯π‘₯) 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, 𝑓𝑓(π‘₯π‘₯) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙, 𝑓𝑓(π‘₯π‘₯) = 𝑙𝑙𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 π‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘ž , 𝑓𝑓(π‘₯π‘₯) = π‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘ž 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 and 𝑓𝑓(π‘₯π‘₯) = π‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘ž π‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘žπ‘ž 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-


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