Domaine De Définition D’une Fonction

1. Quel est le domaine de définition de la fonction représentée ci-contre ?

Dom f = [1 ; 5]

Dom f = ]1 ; 5[

Dom f = [-5 ; 3]

Dom f = ]-5 ; 3[

The given correct answer, "Dom f = [-5 ; 3]", represents the domain of the function represented in the graph. It indicates that the function is defined for all values of x between -5 and 3, including the endpoints. This means that any x-value within this range can be plugged into the function to obtain a valid output.

Explanation

The given correct answer, "Dom f = [-5 ; 3]", represents the domain of the function represented in the graph. It indicates that the function is defined for all values of x between -5 and 3, including the endpoints. This means that any x-value within this range can be plugged into the function to obtain a valid output.

2. Quel est le domaine de définition de la fonction ci-dessous?

Dom f = =]-3;5]

Dom f = ]-3;5[

Dom f = [-3;5[

Dom f = [-3;5]

The correct answer is Dom f = [-3;5[. This answer indicates that the domain of the function includes all real numbers greater than or equal to -3 and less than 5, including -3 but excluding 5.

Explanation

The correct answer is Dom f = [-3;5[. This answer indicates that the domain of the function includes all real numbers greater than or equal to -3 and less than 5, including -3 but excluding 5.

3. Le domaine de définition d'une fonction comprenant une racine d'indice pair s'ecrit ...

....sous forme d’un ensemble de nombre.

...sous forme d’intervalle.

....sous forme d’un ensemble de nombre excluant certains d’entre eux.

The correct answer is "sous forme d’intervalle." This is because when the domain of a function includes a root with an even index, it is typically expressed as an interval. An interval represents a range of numbers between two specific values, which is suitable for representing the domain of a function with an even root.

Explanation

The correct answer is "sous forme d’intervalle." This is because when the domain of a function includes a root with an even index, it is typically expressed as an interval. An interval represents a range of numbers between two specific values, which is suitable for representing the domain of a function with an even root.

4. Pour une fraction, la condition d'existence est :

Le numérateur doit être différent de 0.

Le numérateur et le dénominateur doit être différent de 0.

Le dénominateur doit être différent de 0.

Le dénominateur doit être supérieur à 0.

The correct answer is "Le dénominateur doit être différent de 0." This is because in a fraction, the denominator represents the number of equal parts the whole is divided into. If the denominator is 0, it means there are no parts or the division is not possible, which makes the fraction undefined. Therefore, the denominator must always be a non-zero value for the fraction to exist.

Explanation

The correct answer is "Le dénominateur doit être différent de 0." This is because in a fraction, the denominator represents the number of equal parts the whole is divided into. If the denominator is 0, it means there are no parts or the division is not possible, which makes the fraction undefined. Therefore, the denominator must always be a non-zero value for the fraction to exist.

5. Dans une fonction comprenant une racine d'indice pair,

le radicand doit être strictement supérieur à 0.

le radicand doit être différent de 0.

le radicand doit être supérieur ou égal à 0.

The correct answer is "le radicand doit être supérieur ou égal à 0." This is because in a function with an even index root, the radicand must be greater than or equal to 0. This is because even index roots, such as square roots (index 2), can only be taken of non-negative numbers. Taking the even index root of a negative number would result in an imaginary number. Therefore, the radicand must be either positive or zero.

Explanation

The correct answer is "le radicand doit être supérieur ou égal à 0." This is because in a function with an even index root, the radicand must be greater than or equal to 0. This is because even index roots, such as square roots (index 2), can only be taken of non-negative numbers. Taking the even index root of a negative number would result in an imaginary number. Therefore, the radicand must be either positive or zero.

6. Dans le cours de 4^e, il y a des conditions d'existence....

... dans toutes les fonctions comprenant une racine.

...dans toutes les fonctions.

...dans toutes les fonctions comprenant une racine d’indice impair.

...dans les fonctions comprenant une fraction, une racine d’indice paire ou les deux.

The correct answer is "...dans les fonctions comprenant une fraction, une racine d’indice paire ou les deux." This answer states that there are conditions of existence in functions that include a fraction, an even root, or both. This implies that certain functions may not have a defined solution or may have restrictions on their domain if they contain these elements.

Explanation

The correct answer is "...dans les fonctions comprenant une fraction, une racine d’indice paire ou les deux." This answer states that there are conditions of existence in functions that include a fraction, an even root, or both. This implies that certain functions may not have a defined solution or may have restrictions on their domain if they contain these elements.