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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, where the denominator is not 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, representing the divisor and determining domain restrictions.
  • Domain
    The set of all real numbers for which a function is defined, excluding values that make the denominator zero.
  • Domain Restriction
    A 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, specifying which values are included or excluded.
  • Lowest Terms
    The simplest form of a rational function, achieved by factoring and canceling common factors in numerator and denominator.
  • Factoring
    The process of expressing a polynomial as a product of its simpler components, often used to simplify rational functions.
  • Difference of Squares
    A special factoring pattern where a squared term is subtracted from another squared term, resulting in two binomial factors.
  • Common Factor
    A factor that appears in both the numerator and denominator, which can be canceled to simplify a rational function.
  • Real Number
    Any value on the continuous number line, including both rational and irrational numbers, used in defining domains.
  • Simplification
    The process of reducing a rational function to its most basic form by canceling common factors.
  • Restriction
    A specific value that is not allowed in the domain due to causing division by zero in the denominator.
  • Greatest Common Factor
    The largest factor shared by terms in a polynomial, useful for factoring and simplifying rational functions.