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Function Operations definitions

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  • Function
    A mathematical rule assigning each input exactly one output, often written as f(x) or g(x).
  • Domain
    The set of all input values for which a function is defined, considering any restrictions like division by zero.
  • Range
    The set of all possible output values a function can produce based on its domain.
  • Polynomial
    An algebraic expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication.
  • Like Terms
    Terms in an expression that have identical variable parts and can be combined through addition or subtraction.
  • Square Root
    A value that, when multiplied by itself, gives the original number; introduces domain restrictions to non-negative inputs.
  • Denominator
    The bottom part of a fraction, whose value cannot be zero to avoid undefined expressions.
  • Interval Notation
    A mathematical notation used to describe the set of values within a domain, such as (0, ∞) or (−∞, 2).
  • Difference of Squares
    An algebraic pattern where an expression like a^2 − b^2 factors into (a + b)(a − b).
  • FOIL Method
    A technique for multiplying two binomials by multiplying First, Outside, Inside, and Last terms.
  • Fraction
    A mathematical expression representing division, with a numerator above and a denominator below a dividing line.
  • Notation
    The system of symbols and formats used to represent mathematical operations, such as f+g(x) or f/g(x).
  • Restriction
    A limitation on the domain of a function, often due to operations like division by zero or taking square roots of negatives.
  • Simplification
    The process of rewriting an expression in a more compact or easily interpretable form, often after performing operations.
  • Real Numbers
    All numbers on the continuous number line, including both rational and irrational values, often forming the domain of polynomials.