Rational Functions

This chapter will study the characteristics and techniques of sketching rational functions. While rational functions exhibit different properties than polynomial functions, they are considered combinations of polynomial functions. Therefore, to some extent, previous chapters’ concepts will interfere with the ones studied in this chapter. The chapter will begin from describing the rational functions’ long-run behaviors, followed by the short-run behavior. In addition to finding functions’ intercepts, SR behavior will include the technique of assessing function’s one-sided limits and discontinuity. Combining these behaviors into one general technique of analyzing and sketching rational functions will culminate in the first sections of this chapter. Rational functions with their characteristic asymptotic behavior have many applications. Modeling with rational functions supported by covariational reasoning with real contexts will conclude this chapter.