Question

Select all representations for the domain of a function given by the number of hours slept in one day. (2 points) Responses [0, ∞)[0, ∞)[0, ∞)[0, ∞) {x | 0≤ x ≤24}{x | 0≤ x ≤24}{x | 0≤ x ≤24}{x | 0≤ x ≤24} (24, ∞)(24, ∞)(24, ∞)(24, ∞) (0, 24)(0, 24)(0, 24)(0, 24) [0, 24][0, 24][0, 24][0, 24] {x| x∈R}{x| x∈R}{x| x∈R}{x| x∈R} {x| x>24}

Answer 1

The domain of a function representing the number of hours slept in one day should be between 0 and 24 hours, inclusive, since a person cannot sleep for negative hours and cannot sleep more than 24 hours in one day.

The valid representations for the domain are:

1. \([0, 24]\) - This includes 0 hours and 24 hours, representing the full range of possible sleep hours.
2. \({x | 0 \leq x \leq 24}\) - This is another way to represent the same range in set notation.

The other options like \((0, 24)\), \((24, \infty)\), and \({x | x \in R}\) do not adequately represent the domain of sleeping hours since they either exclude valid values or include impossible ones.

So the valid representations are:

• \([0, 24]\)
• \({x | 0 \leq x \leq 24}\)