Answer:
Step-by-step explanation:
To determine the domain and range of the function \( y = 24 - x \), which models the number of waking hours in a day when a person sleeps for \( x \) hours, we need to consider the constraints of the problem.
Domain:
- In this context, the domain represents the possible values for \( x \), the number of hours a person sleeps.
- Since a day has 24 hours and the person is sleeping, \( x \) must be between 0 and 24 hours.
- So, the domain is \( 0 \leq x \leq 24 \).
Range:
- The range represents the possible values for \( y \), the number of waking hours.
- Since waking hours are calculated as the total hours in a day (24) minus the hours spent sleeping (\( x \)), the range will be the values of \( y \) obtained by substituting the values of \( x \) within the domain.
- As \( x \) varies from 0 to 24, \( y \) will vary from 24 to 0.
- So, the range is \( 0 \leq y \leq 24 \).
In summary:
- Domain: \( 0 \leq x \leq 24 \)
- Range: \( 0 \leq y \leq 24 \)
