Functions

Question	Answer
A linear /ˈlɪniə(r)/ function	Une fonction affine
The function ln	The logarithm /ˈlɒɡərɪðəm/ function/the natural logarithm
A one-to-one function	Une bijection
The edges of the domain (of a function)	Les bornes de l'ensemble de définition d'une fonction
What is the input value for which $f(x)=0$ ?	Quels sont les antécédents de 0 par $f$ ?
Remplacer $x$ par 0	Plug in 0 for $x$ = Plug in $x=0$
The range of a function	The complete set of all possible resulting values of the dependent variable ( $y$ - usually)- after we have substituted the domain.
The graph of $f$ passes through $(1-0)$	Le graphique de $f$ passe par le point de coordonnées $(1\pv 0)$
The slope	The ratio of the vertical change between two points- the rise- to the horizontal change between the same two points- the run
The slope of a line passing through the points $(x_1- y_1)$ and $(x_2- y_2)$ is	$m=\dfrac{y_2-y_1}{x_2-x_1}$
A line with a positive slope $(m > 0)$	A line which rises from left to right
A line with a negative slope $(m < 0)$	A line which falls from left to right
The slope intercept form of a linear function	$y=mx+b$ - $m=\text{slope}$ - $b=y−\text{intercept}$
The point-slope form of the equation of a straight line	$y−y_1 = m(x − x_1)$
The slope-intercept form of the equation of a straight line	$y=mx+p$
The inverse function of $f$	La fonction réciproque de $f$
$\displaystyle\lim_{x\to\infty} f(x)$	Limit of $f(x)$ as $x$ approaches infinity
To sketch the graph of $f$	Donner une allure de la représentation graphique de $f$
To graph the function $f$	Tracer précisément la représentation graphique de $f$
The function $f$ is differentiable /dɪfə'renʃieɪbl/ on $\mathbb{R}$	La fonction $f$ est dérivable sur $\mathbb{R}$ .
To differentiate /dɪfəˈrenʃieɪt/ the function $f$	Dériver le fonction $f$
$f'$ est la dérivée de la fonction $f$	$f'$ is the (first) derivative /dɪˈrɪvətɪv/ of the function $f$
$y'=\dfrac{\text{d} y}{\text{d} x}$ is the derivative /dɪˈrɪvətɪv/ of $y$ with respect to $x$	La dérivée de $y$ par rapport à $x$
$f'(2)$ est la dérivée de $f$ en 2	$f'(2)$ is the derivative of $f$ at 2/the derivative of $f$ at $x=2$ /the derivative of $f$ at the point 2
$f''$ est la dérivée seconde de $f$	$f''$ is the second derivative /dɪˈrɪvətɪv/ of the function $f$
$f'(x)$	$f$ dash $x$ or the (first) derivative of $f$ with respect to $x$ or $f$ prime of $x$
$f''(x)$	$f$ double-dash $x$ or the second derivative of $f$ with respect to $x$ or $f$ double prime of $x$
If $y=f(x)$ - $y$ is called	The image of $x$ under $f$
If $y=f(x)$ - $y$ is called- $x$ is called	A preimage /pri:ɪmɪdʒ/ of $y$ under $f$
When talking about limits- $0\cdot \infty$ is called	An indeterminate /ɪndɪˈtɜːmɪnət/ form
Sketch the graph of the function $f$	Dessine le graphique de la fonction $f$ .
A piecewise function (or a piecewise-defined function)	Une fonction définie par morceaux
A constant piecewise function	Une fonction constante par morceaux
To graph a function	Tracer la représentation graphique d'une fonction
The function that assigns to each nonnegative integer its last digit	Une fonction qui associe à chaque entier naturel son dernier chiffre
The function is concave /kɒnˈkeɪv/ up/the function is convex	La fonction est convexe
The function is concave /kɒnˈkeɪv/ down	La fonction est concave
The difference quotient of $f$ is the average rate of change of $f(x)$ over the interval $[x-x+h]$	Le taux d'accroissement de $f$ entre $x$ et $x+h$
A limit exists if and only if	Its left-hand and right-hand limits exist and agree
An invertible /ɪnˈvɜːtəbəl/ function	Une fonction bijective
If $f$ is an invertible /ɪnˈvɜːtəbəl/ function	Its graph passes the horizontal line test
The graph of $y=x^{1/n}$ is obtained	By reflecting the graph of $y=x^n$ across the line $y=x$
$\csc(x)$	$\dfrac{1}{\sin(x)}$
$\sec(x)$	$\dfrac{1}{\cos(x)}$
$\cot(x)$	$\dfrac{1}{\tan(x)}$
If $f(x)$ is continuous at $x=a$	Then the graph of $f(x)$ can be drawn by hand around $x=a$ without having to lift the pencil from the paper.
The greatest integer function is denoted by $\lfloor x\rfloor$	La fonction partie entière
A bounded function	Une fonction bornée
An anti-derivative of the function $f$	Une primitive de la fonction $f$

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