Introduction to Rational Functions definitions Flashcards
Introduction to Rational Functions definitions
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Rational Function A mathematical expression formed by dividing one polynomial by another, with the denominator not equal to zero. Polynomial An algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Numerator The top part of a fraction, representing the dividend in a rational function. Denominator The bottom part of a fraction, whose value cannot be zero in a rational function. Domain The set of all real numbers for which a function is defined, excluding values that make the denominator zero. Domain Restriction A specific value or values of the variable that are excluded from the domain because they make the denominator zero. Set Notation A mathematical format used to describe the domain, often written as x such that x does not equal certain values. Lowest Terms The simplest form of a rational function, achieved by factoring and canceling common factors in the numerator and denominator. Common Factor A factor that appears in both the numerator and denominator, which can be canceled to simplify a rational function. Difference of Squares A special factoring pattern where an expression is written as a squared term minus another squared term, factored as (a+b)(a-b). Greatest Common Factor The largest factor shared by all terms in a polynomial, used to simplify expressions. Real Number Any value on the continuous number line, including both rational and irrational numbers, used in defining domains. Factoring The process of expressing a polynomial as a product of its factors to aid in simplification. Fraction A mathematical expression representing the division of one quantity by another, central to rational functions. Restriction A limitation placed on the variable to prevent undefined values, especially those causing division by zero.
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