38910499
Description
Flashcards by Dominique TREMULOT, updated 9 months ago
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Created by Dominique TREMULOT
9 months ago
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| 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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