Rational functions are functions that can be expressed as the ratio of two polynomials, typically written in the form $$R(x) = \frac{P(x)}{Q(x)}$$ where $$P(x)$$ and $$Q(x)$$ are polynomials and $$Q(x) \neq 0$$. These functions are important because they can exhibit unique behaviors such as asymptotes, discontinuities, and varying end behavior. Understanding rational functions helps in analyzing their limits, differentiating them, and applying the Intermediate Value Theorem effectively.
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