Select all representations for the domain of a function given by the number of hours slept in one day.
Responses
[0, 24]
[0, 24]
{x | 0≤ x ≤24}
{x | 0≤ x ≤24}
{x| x∈R}
{x| x∈R}
[0, ∞)
[0, ∞)
{x| x>24}
{x| x>24}
(0, 24)
(0, 24)
(24, ∞)
To determine the domain of a function, we need to identify the possible input values that the function can accept. In this case, the function represents the number of hours slept in one day.
The domain typically represents the set of real numbers that are valid inputs for the function. In this case, the number of hours slept cannot be negative, so we can eliminate any negative values from the domain.
We also know that a day has 24 hours, and the number of hours slept cannot exceed this limit. Therefore, we need to include any values between 0 and 24.
Based on the given options:
[0, 24] - This option includes all values from 0 to 24, which are valid hours for sleep. This representation uses square brackets to indicate that both 0 and 24 are included.
{x | 0≤ x ≤24} - This option represents the same range, using set notation. It indicates that x belongs to the real numbers (represented by "x ∈ R") and satisfies the inequality 0 ≤ x ≤ 24.
[0, ∞) - This option includes all values from 0 to positive infinity. However, since we know that the number of hours slept in one day cannot exceed 24, this representation is not accurate.
{x| x>24} - This option includes values greater than 24, which implies that the number of hours slept can exceed a day. Since we are looking for the number of hours slept in one day, this representation is not valid.
(0, 24) - This option includes all values between 0 and 24, excluding the endpoints. This means that 0 and 24 are not included in the domain. However, since the question asks for all possible representations, this option should be considered as well.
(24, ∞) - This option includes all values greater than 24. Since we are dealing with the number of hours slept in one day, this representation is not valid.
Therefore, the correct representations for the domain of the function are:
[0, 24] and
(0, 24)
[0, 24]
{x | 0≤ x ≤24}
{x| x∈R}
[0, ∞)
(0, 24)
The representations for the domain of a function given by the number of hours slept in one day are:
[0, 24]
{x | 0≤ x ≤24}
{x| x∈R}
[0, ∞)
(0, 24)