Question

Grace works between 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours is given by the function f(t) = 12t, where 5 ≤ t ≤ 15.

Find the range and domain.

Answer 1

The domain of Grace's function is 10 ≤ t ≤ 20. The range of Grace's function is 90 ≤ g(t) ≤ 180. The domain of Frances's function is 5 ≤ t ≤ 15. The range of Frances's function is 60 ≤ f(t) ≤ 180.

Step-by-step explanation:

The domain of Grace's function, g(t), is the set of possible values for t, which represents the number of hours she works per week. Since Grace works between 10 to 20 hours per week, the domain of g(t) is 10 ≤ t ≤ 20. The range of g(t) is the set of possible values for her earnings, which is determined by multiplying the number of hours she works (t) by her hourly rate ($9.00). Therefore, the range of g(t) is 10 * 9 ≤ g(t) ≤ 20 * 9, or 90 ≤ g(t) ≤ 180.

The domain of Frances's function, f(t), is the set of possible values for t, which represents the number of hours she works. Given that 5 ≤ t ≤ 15, this is the domain of f(t). The range of f(t) is the set of possible values for her earnings, which is determined by multiplying the number of hours she works (t) by her hourly rate (12). Therefore, the range of f(t) is 5 * 12 ≤ f(t) ≤ 15 * 12, or 60 ≤ f(t) ≤ 180.