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Combining Functions definitions

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  • Function
    A rule assigning each input exactly one output, often expressed as f(x), with a specific domain and range.
  • Domain
    The set of all input values for which a function is defined, often restricted by denominators or square roots.
  • Range
    The set of all possible output values a function can produce based on its domain.
  • Polynomial
    An algebraic expression involving sums of powers of x with real coefficients, such as x² + 5x + 7.
  • Composition
    A process where the output of one function becomes the input of another, denoted as f(g(x)).
  • Notation
    A symbolic representation of mathematical operations, such as f+g(x), f∘g(x), or f/g(x).
  • Like Terms
    Terms in algebraic expressions with identical variable parts, which can be combined during addition or subtraction.
  • Denominator
    The bottom part of a fraction, whose value cannot be zero to avoid undefined expressions.
  • Square Root
    An operation that finds a number which, when multiplied by itself, gives the original value; its argument must be non-negative.
  • Interval Notation
    A concise way to describe sets of numbers, such as (0, ∞) for all positive real numbers.
  • Difference of Squares
    An algebraic identity where a² - b² factors into (a + b)(a - b).
  • Shortcut Method
    A technique for evaluating composed functions by plugging values into the inner function first, then into the outer.
  • Restriction
    A limitation on the domain, often due to denominators equaling zero or negative values under square roots.
  • FOIL Method
    A process for multiplying two binomials: First, Outer, Inner, Last terms are multiplied and summed.
  • Interval
    A continuous set of real numbers between two endpoints, possibly including or excluding the endpoints.