# Une fonction affine ---- ## A linear /ˈlɪniə[r]/ function --- # The logarithm /ˈlɒɡərɪðəm/ function/the natural logarithm ---- ## The function ln --- # Une bijection ---- ## A one-to-one function --- # Les bornes de l'ensemble de définition d'une fonction ---- ## The edges of the domain (of a function) --- # Quels sont les antécédents de 0 par $f$ ? ---- ## What is the input value for which $f(x)=0$? --- # Plug in 0 for $x$ = Plug in $x=0$ ---- ## Remplacer $x$ par 0 --- # The complete set of all possible resulting values of the dependent variable ($y$- usually)- after we have substituted the domain ---- ## The range of a function --- # Le graphique de $f$ passe par le point de coordonnées $(1;0)$ ---- ## The graph of $f$ passes through $(1,0)$ --- # The ratio of the vertical change between two points- the rise- to the horizontal change between the same two points- the run ---- ## The slope --- # $m=\dfrac{y_2-y_1}{x_2-x_1}$ ---- ## The slope of a line passing through the points $(x_1- y_1)$ and $(x_2- y_2)$ is --- # A line which rises from left to right ---- ## A line with a positive slope $(m > 0)$ --- # A line which falls from left to right ---- ## A line with a negative slope $(m < 0)$ --- # $y=mx+b$ - $m=\text{slope}$ - $b=y−\text{intercept}$ ---- ## The slope intercept form of a linear function --- # $y−y_1 = m(x − x_1)$ ---- ## The point-slope form of the equation of a straight line --- # $y=mx+p$ ---- ## The slope-intercept form of the equation of a straight line --- # La fonction réciproque de $f$ ---- ## The inverse function of $f$ --- # $\displaystyle\lim_{x\to\infty} f(x)$ ---- ## Limit of $f(x)$ as $x$ approaches infinity --- # Donner une allure de la représentation graphique de $f$ ---- ## To sketch the graph of $f$ --- # Tracer précisément la représentation graphique de $f$ ---- ## To graph the function $f$ --- # La fonction $f$ est dérivable sur $\mathbb{R}$. ---- ## The function $f$ is differentiable /dɪfə'renʃieɪbl/ on $\mathbb{R}$ --- # Dériver le fonction $f$ ---- ## To differentiate /dɪfəˈrenʃieɪt/ the function $f$ --- # $f'$ est la dérivée de la fonction $f$ ---- ## $f'$ is the (first) derivative /dɪˈrɪvətɪv/ of the function $f$ --- # La dérivée de $y$ par rapport à $x$ ---- ## $y'=\dfrac{\text{d} y}{\text{d} x}$ is the derivative /dɪˈrɪvətɪv/ of $y$ with respect to $x$ --- # $f'(2)$ 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 $y=f(x)$, $x$ is called ---- ## A preimage /pri:ɪmɪdʒ/ of $y$ under $f$ --- # An indeterminate /ɪndɪˈtɜːmɪnət/ form ---- ## When talking about limits, $0\cdot \infty$ is called --- # Dessine le graphique de la fonction $f$ ---- ## Sketch the graph of the function $f$ --- # Une fonction définie par morceaux ---- ## A piecewise function (or a piecewise-defined function) --- # Une fonction constante par morceaux ---- ## A constant piecewise function --- # Tracer la représentation graphique d'une fonction ---- ## To graph a function --- # Une fonction qui associe à chaque entier naturel son dernier chiffre ---- ## The function that assigns to each nonnegative integer its last digit --- # La fonction est convexe ---- ## The function is concave /kɒnˈkeɪv/ up/the function is convex --- # La fonction est concave ---- ## The function is concave /kɒnˈkeɪv/ down --- # Le taux d'accroissement de $f$ entre $x$ et $x+h$ ---- ## The difference quotient of $f$ is the average rate of change of $f(x)$ over the interval $[x,x+h]$ --- # A limit exists if and only if ---- ## Its left-hand and right-hand limits exist and agree --- # Une fonction bijective ---- ## An invertible /ɪnˈvɜːtəbəl/ function --- # If $f$ is an invertible /ɪnˈvɜːtəbəl/ function ---- ## Its graph passes the horizontal line test --- # By reflecting the graph of $y=x^n$ across the line $y=x$ ---- ## The graph of $y=x^{1/n}$ is obtained --- # $\dfrac{1}{\sin(x)}$ ---- ## $\csc(x)$ --- # $\dfrac{1}{\cos(x)}$ ---- ## $\sec(x)$ --- # $\dfrac{1}{\tan(x)}$ ---- ## $\cot(x)$ --- # 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 --- # La fonction partie entière ---- ## The greatest integer function is denoted by $\lfloor x\rfloor$ --- # Une fonction bornée ---- ## A bounded function --- # Une primitive de la fonction $f$ ---- ## An anti-derivative of the function $f$ --- # Une chaîne ---- ## A catenary /kəˈtiːnərɪ/ --- # Un sommet (pour la courbe d'une fonction) ---- ## A turning point --- # Nous allons modéliser l'arche en utilisant une parabole et voir si cela correspond bien ---- ## We will model the arch using a parabola /pəˈræbələ/ and see how well it fits --- # Le tableau de variations de la fonction $f$ ---- ## The variation /veəriˈeɪʃn/ table of the function $f$ <style> .slides {background-image:url("https://raw.githubusercontent.com/tremulotmaths/latex/master/von_koch_transparent.png");} .slides h1 {padding:2em; font-family:Arial; background-color:#133E29; opacity: 0.9;color:white; font-size:1em!important;} .slides h2 {background:#131750 ; opacity: 0.9;padding : 2em 0.2em; color:white; font-size:1em!important;} .slides h4 {margin-bottom:1.5em} </style>