{
  "unit": 1,
  "title": "Advanced Functions, Transformations & Inverses",
  "terms": [
    {
      "en": "function",
      "es": "función",
      "fr": "fonction",
      "ar": "دالة",
      "pt": "função",
      "definition": "A relation assigning each permitted input exactly one output."
    },
    {
      "en": "function notation",
      "es": "notación de funciones",
      "fr": "notation fonctionnelle",
      "ar": "ترميز الدوال",
      "pt": "notação de função",
      "definition": "The notation f(x) denotes the output of function f at input x, not f multiplied by x."
    },
    {
      "en": "domain",
      "es": "dominio",
      "fr": "domaine de définition",
      "ar": "مجال الدالة",
      "pt": "domínio",
      "definition": "The set of all permissible input values."
    },
    {
      "en": "range",
      "es": "recorrido",
      "fr": "ensemble des valeurs",
      "ar": "مدى الدالة",
      "pt": "imagem",
      "definition": "The set of outputs actually produced by inputs in the domain."
    },
    {
      "en": "interval notation",
      "es": "notación de intervalos",
      "fr": "notation des intervalles",
      "ar": "ترميز الفترات",
      "pt": "notação de intervalos",
      "definition": "A compact way to describe a real-number set using endpoints, brackets, and parentheses."
    },
    {
      "en": "function transformation",
      "es": "transformación de funciones",
      "fr": "transformation de fonction",
      "ar": "تحويل الدوال",
      "pt": "transformação de funções",
      "definition": "A change to a graph caused by shifting, reflecting, or stretching its parent function."
    },
    {
      "en": "parent function",
      "es": "función madre",
      "fr": "fonction de référence",
      "ar": "الدالة الأم",
      "pt": "função-mãe",
      "definition": "A basic reference function from which transformed functions are derived."
    },
    {
      "en": "vertical translation",
      "es": "traslación vertical",
      "fr": "translation verticale",
      "ar": "إزاحة رأسية",
      "pt": "translação vertical",
      "definition": "A change f(x) to f(x)+k, shifting all y-values by k."
    },
    {
      "en": "horizontal translation",
      "es": "traslación horizontal",
      "fr": "translation horizontale",
      "ar": "إزاحة أفقية",
      "pt": "translação horizontal",
      "definition": "A change f(x) to f(x-h), shifting the graph right by h."
    },
    {
      "en": "function composition",
      "es": "composición de funciones",
      "fr": "composition de fonctions",
      "ar": "تركيب الدوال",
      "pt": "composição de funções",
      "definition": "The operation (f∘g)(x)=f(g(x)), requiring g(x) to lie in the domain of f."
    },
    {
      "en": "function decomposition",
      "es": "descomposición de funciones",
      "fr": "décomposition de fonctions",
      "ar": "تحليل الدالة إلى مركبات",
      "pt": "decomposição de funções",
      "definition": "Writing a function as a composition of simpler functions."
    },
    {
      "en": "inverse function",
      "es": "función inversa",
      "fr": "fonction réciproque",
      "ar": "الدالة العكسية",
      "pt": "função inversa",
      "definition": "A function that reverses the input-output correspondence of a one-to-one function."
    },
    {
      "en": "one-to-one function",
      "es": "función inyectiva",
      "fr": "fonction injective",
      "ar": "دالة واحد لواحد",
      "pt": "função injetiva",
      "definition": "A function whose distinct inputs always yield distinct outputs; it passes the horizontal-line test."
    },
    {
      "en": "piecewise function",
      "es": "función definida a trozos",
      "fr": "fonction définie par morceaux",
      "ar": "دالة معرفة على أجزاء",
      "pt": "função definida por partes",
      "definition": "A function given by different rules on specified parts of its domain."
    },
    {
      "en": "absolute-value function",
      "es": "función de valor absoluto",
      "fr": "fonction valeur absolue",
      "ar": "دالة القيمة المطلقة",
      "pt": "função de valor absoluto",
      "definition": "A function involving the absolute value of an input, which measures its nonnegative distance from zero."
    },
    {
      "en": "step function",
      "es": "función escalonada",
      "fr": "fonction en escalier",
      "ar": "دالة درجية",
      "pt": "função degrau",
      "definition": "A piecewise-constant function with fixed output levels on intervals."
    }
  ],
  "schema_version": "1.1"
}