Final answer:
a. Zero is in the domain and range of H. b. An appropriate domain and range for H are the set of non-negative integers, including zero.
Step-by-step explanation:
a. The domain of H represents the input values or the days into the school year. Since the number of homework problems assigned can be calculated for any number of days into the school year, including zero, the number zero is in the domain of H (zero is in the domain of H). The range of H represents the output values or the number of homework problems assigned. Since the number of homework problems can be any non-negative integer, including zero, zero is also in the range of H (zero is in the range of H).
b. An appropriate domain for H would be the set of non-negative integers, since the number of homework problems assigned cannot be negative. The range of H would also be the set of non-negative integers, including zero, since the number of homework problems assigned cannot be negative.