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Function Operations definitions

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  • Function Operations
    Processes involving addition, subtraction, multiplication, or division applied to two or more functions, often requiring domain analysis.
  • Domain
    Set of all input values for which a function or a combination of functions is defined, considering restrictions like denominators and square roots.
  • Polynomial
    Algebraic expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication.
  • Radical Function
    Function containing a root, such as a square root, which imposes restrictions on the domain to avoid negative values under the root.
  • Denominator
    Bottom part of a fraction; values making this zero are excluded from the domain to prevent undefined expressions.
  • Like Terms
    Terms in algebraic expressions with identical variable parts, which can be combined during addition or subtraction.
  • Interval Notation
    Mathematical notation using brackets and parentheses to describe sets of numbers, especially domains.
  • Difference of Squares
    Algebraic pattern where an expression like a^2 - b^2 factors into (a + b)(a - b).
  • Notation
    Symbols or formats such as f+g(x), f-g(x), f*g(x), or f/g(x) used to represent operations on functions.
  • Range
    Set of all possible output values a function can produce, often considered alongside the domain.
  • Restriction
    Condition that limits the domain of a function, often due to denominators or expressions under radicals.
  • Intersection
    Set of values common to the domains of two or more functions, forming the domain of their combined operation.
  • Square Root
    Radical expression requiring the radicand to be non-negative, influencing the domain of the function.
  • FOIL Method
    Technique for multiplying two binomials: First, Outer, Inner, Last, used to expand expressions.
  • Simplification
    Process of combining like terms and reducing expressions to their most concise form after performing operations.