Function vocabulary

Fonction / Function, map, mapping

• abscisse (d’un point), ordonnée / x-coordinate, y-coordinate
• accolade / brace
• analyse (en tant que domaine des  mathématiques) / calculus
• axe des abscisses, axe des ordonnées  / x-axis, y-axis
• coefficient directeur / slope
• cosinus, sinus / cosine, sine
• courbe paramétrée / parametric curve
• courbe représentative / graph
• associer y à x / to map x onto y
• antécédent / pre-image (less frequently : counterimage or inverse image)
• comportement aux infinis (d’une fonction) / end behaviour
• continu (par morceaux) / (piecewise) continuous
• décroissance exponentielle / exponential decay
• dérivée / derivative
• dériver / to differentiate
• fonction / function, map, mapping
• Injective, bijective, surjective
  • fonction bijective / bijective function, one-to-one correspondence (≠ one-to-one function)
  • fonction injective / injective function, one-to-one function (≠ one-to-one correspondence cf. above)
  • fonction surjective / surjective function, onto function
      
• forme canonique (d’un polynôme du second degré) / vertex form
• la limite de f (x) quand x tend vers a est l / the limit of f as x approaches a equals/is l
• fonction définie par morceaux / piecewise-defined function
  • a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
• ordonnée à l’origine / y-intercept
• point d’inflexion / inflection point
• primitive / antiderivative, primitive function, indefinite integral
• système de coordonnées, repère / coordinate system

Monotonie / monotonic, monotone function

• fonction croissante / increasing function or nondecreasing function
• fonction décroissante / decreasing function or nonincreasing function 
• fonction monotone / monotonic function, monotone function
  
  • In calculus, a function f$f$ defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing.
  • A function is called monotonically increasing (also increasing or non-decreasing), if for all x$x$ and y$y$ such that x≤y${\displaystyle x\le y}$ one has f(x)≤f(y)${\displaystyle f\left(x\right)\le f\left(y\right)}$, so f$f$ preserves the order .
  • Likewise, a function is called monotonically decreasing (also decreasing or non-increasing) if for all x$x$ and y$y$ such that x≤y${\displaystyle x\le y}$ one has f(x)≥f(y)${\displaystyle f\left(x\right)\ge f\left(y\right)}$,, so it reverses the order
• Attention, l’anglais est trompeur ici : la négation de « f$f$ est croissante » n’est pas « f$f$ est décroissante » et réciproquement.

Fonction affine et linéaire

• Fonctions affines / linear function (or affine)
  
  • coefficient directeur / slope
  • ordonnée à l'origine / y-intercept
• Fonctions linéaires /  homogeneous linear function  
  • A linear function is a polynomial function in which the variable x has degree at most one: f(x)=ax+b$f(x)=ax+b$ .
  • Such a function is called linear because its graph, the set of all points (x,f(x))$(x,f(x))$ in the Cartesian plane, is a line.
  • The coefficient a is called the slope of the function and of the line (see below)
  • The coefficient b is called the y-intercept
  • If the slope is a=0$a=0$ , this is a constant function f(x)=b$f(x)=b$ defining a horizontal line, which some authors exclude from the class of linear functions.
  • If b=0$b=0$ then the linear function is said to be homogeneous.
    
    • Such function defines a line that passes through the origin of the coordinate system, that is, the point (x,y)=(0,0)$(x,y)=(0,0)$ .
  • In advanced mathematics texts, the term linear function often denotes specifically homogeneous linear functions, while the term affine function is used for the general case, which includes b≠0$b\ne 0$.

Fonction inverse, fonction réciproque, opposé 

• La fonction bijection réciproque (ou fonction réciproque ou réciproque) / the inverse function of
  
  • In mathematics, the inverse function of a function f$f$ (also called the inverse of f$f$) is a function that undoes the operation of f$f$.
  • The inverse of f$f$ exists if and only if f$f$ is bijective, and if it exists, is denoted by f−1${\displaystyle f^{-1}}$.
  • The inverse sine of x$x$ denoted by sin−1x$si{n}^{-1}x$  or arcsinx$\arcsin x$.
  • The function f$f$ is invertible if and only if it is bijective.
     
• La fonction inverse : x⟼1x$x⟼{\displaystyle \frac{1}{x}}$ / the reciprocal function
  
  • The reciprocal function, the function f$f$ that maps x$x$ to 1x${\displaystyle \frac{1}{x}}$, is one of the simplest examples of a function which is its own inverse (an involution).
  • The reciprocal function: y=1/x$y=1/x$. For every x$x$ except 0, y$y$ represents its multiplicative inverse. The graph forms a rectangular hyperbola.

• Inverse d'un nombre, d'une fonction / multiplicative inverse or reciprocal ou just inverse
  

  • In mathematics, a multiplicative inverse or reciprocal for a number x$x$, denoted by 1x${\displaystyle \frac{1}{x}}$ or x−1$x^{-1}$, is a number which when multiplied by x$x$ yields the multiplicative identity, 1.

  • In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse).
  • The notation f−1$f^{-1}$ is sometimes also used for the inverse function of the function f(x)$f(x)$, which is not in general equal to the multiplicative inverse.
  • For example, the multiplicative inverse 1sinx=(sinx)−1${\displaystyle \frac{1}{\sin x}}=(sinx{)}^{-1}$ is the cosecant of x$x$, and not the inverse sine of x$x$ denoted by sin−1x$si{n}^{-1}x$  or arcsinx$\arcsin x$.
     
    
• Opposé d'un nombre / additive inverse, opposite number
  • In mathematics, the additive inverse of a number a$a$ is the number that, when added to a$a$, yields zero.
  • This number is also known as the opposite (number), sign change, and negation.
  • For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself.
      
    
• Inverse function rule
  • In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f$f$ in terms of the derivative of f$f$.
  • More precisely, if the inverse of f$f$ is denoted as f−1$f^{-1}$, then the inverse function rule is, in Lagrange's notation :(f−1)′(a)=1f′(f−1)(a)