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Grace works from 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 each week is given by the function f(t)=10t, where 5 ≤ t ≤ 15. Find the domain and range of each function

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Answer/Step-by-step explanation:

Given that Grace works from 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 each week is given by the function f(t)= 10t, where 5 ≤ t ≤ 15.


Part A:


Given that Grace's time is rounded to the nearest quarter of an hour. The domain for Grace is given by {10, 10.25, 10.50, 10.75, - - -, 19.75, 20}.


The range for grace is given by {9(10), 9(10.25), 9(10.50), 9(10.75), - - -, 9(19.75), 9(20)} = {90, 92.25, 94.5, 96.75, - - -, 177.75, 180}


The domain for Frances is given by: 5 ≤ t ≤ 15.


The range for Frances is given by: 10(5) ≤ f(t) ≤ 10(15) = 50 ≤ f(t) ≤ 150.




Part B:


Grace earns $9 per hour and $80 to $180 per week while Frances earns $10 per hour and $50 to $150 per week.

Answer:

Given that Grace works from 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 each week is given by the function f(t)= 10t, where 5 ≤ t ≤ 15.



Part A:



Given that Grace's time is rounded to the nearest quarter of an hour. The domain for Grace is given by {10, 10.25, 10.50, 10.75, - - -, 19.75, 20}.



The range for grace is given by {9(10), 9(10.25), 9(10.50), 9(10.75), - - -, 9(19.75), 9(20)} = {90, 92.25, 94.5, 96.75, - - -, 177.75, 180}



The domain for Frances is given by: 5 ≤ t ≤ 15.



The range for Frances is given by: 10(5) ≤ f(t) ≤ 10(15) = 50 ≤ f(t) ≤ 150.





Part B:



Grace earns $9 per hour and $80 to $180 per week while Frances earns $10 per hour and $50 to $150 per week.




Step-by-step explanation:




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