Continuité - Spécialité
Graphe
Exercice 1 : Déterminer la continuité d'une fonction à partir d'un graphique
Sur les graphiques suivant, cocher les fonctions discontinues sur l'intervalle \([-10; 10]\)
- 1.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return 11/(2 + Math.pow(x, 2));}", [-10, 10], {"stroke": "blue"}]]}
- 2.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return x*(-1 - x - Math.pow(x, 2)/10)/Math.abs(x);}", [-10, 0], {"stroke": "blue"}], ["function(x){ return x*(-1 - x - Math.pow(x, 2)/10)/Math.abs(x);}", [0, 10], {"stroke": "blue"}]]}
- 3.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return 4 - Math.pow(x, 2)/13;}", [-10, 10], {"stroke": "blue"}]]}
- 4.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return 0.5*x;}", [-10, 10], {"stroke": "blue"}]]}
Exercice 2 : Déterminer la continuité d'une fonction à partir d'un graphique
Voici la représentation graphique d'une fonction \( f \)
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 1], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return Math.abs(-4 + x);}", [-10, 10], {"stroke": "blue"}]]}
En quel(s) point(s) cette fonction est discontinue ?
On donnera la réponse sous la forme d'un ensemble, par exemple \(\{1; 3\}\) ou \([2; 4[\).
Exercice 3 : Déterminer la continuité d'une fonction à partir d'un graphique
Sur les graphiques suivant, cocher les fonctions discontinues sur l'intervalle \([-10; 10]\)
- 1.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return -Math.pow(-3 + Math.pow(x, 2), 1/2);}", [-10, 0], {"stroke": "blue"}], ["function(x){ return -Math.pow(-3 + Math.pow(x, 2), 1/2);}", [0, 10], {"stroke": "blue"}]]}
- 2.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return 4 - Math.pow(x, 2)/14;}", [-10, 10], {"stroke": "blue"}]]}
- 3.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return Math.tan(x);}", [-10, 0], {"stroke": "blue"}], ["function(x){ return Math.tan(x);}", [0, 10], {"stroke": "blue"}]]}
- 4.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return Math.sin(x);}", [-10, 10], {"stroke": "blue"}]]}
Exercice 4 : Déterminer la continuité d'une fonction à partir d'un graphique
Voici la représentation graphique d'une fonction \( f \)
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 1], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return Math.abs(-3 + x);}", [-10, 10], {"stroke": "blue"}]]}
En quel(s) point(s) cette fonction est discontinue ?
On donnera la réponse sous la forme d'un ensemble, par exemple \(\{1; 3\}\) ou \([2; 4[\).
Exercice 5 : Déterminer la continuité d'une fonction à partir d'un graphique
Sur les graphiques suivant, cocher les fonctions continues sur l'intervalle \([-10; 10]\)
- 1.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return -Math.tan(x);}", [-10, 0], {"stroke": "blue"}], ["function(x){ return -Math.tan(x);}", [0, 10], {"stroke": "blue"}]]}
- 2.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return x*(-2 + Math.pow(x, 2)/10)/Math.abs(x);}", [-10, 0], {"stroke": "blue"}], ["function(x){ return x*(-2 + Math.pow(x, 2)/10)/Math.abs(x);}", [0, 10], {"stroke": "blue"}]]}
- 3.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return -Math.cos(x);}", [-10, 10], {"stroke": "blue"}]]}
- 4.
{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30.0, 20.0], "hasGraph": true, "axisArrows": "->", "axisOpacity": 0.5, "gridOpacity": 0.1, "gridStep": [1, 1], "tickStep": [1, 1], "labelStep": [1, 5], "xLabel": "", "yLabel": "", "unityLabels": true}, "plot": [["function(x){ return Math.sin(x);}", [-10, 10], {"stroke": "blue"}]]}