A cloud storage plan charges a flat fee of $20 a month plus $0.25 for every gigabyte (GB) of data used (up to 100 GB maximum). The function 𝐶(𝑔)=0.25𝑔+20C(g)=0.25g+20 models the total cost in dollars of the cell phone plan, where g is the amount of gigabytes you use.What is the domain and range of this function in interval notation within the context of this situation?
Question
A cloud storage plan charges a flat fee of 0.25 for every gigabyte (GB) of data used (up to 100 GB maximum). The function 𝐶(𝑔)=0.25𝑔+20C(g)=0.25g+20 models the total cost in dollars of the cell phone plan, where g is the amount of gigabytes you use.What is the domain and range of this function in interval notation within the context of this situation?
Solution
The domain of the function C(g) = 0.25g + 20 is the set of all possible input values, which in this case is the amount of gigabytes you use. Since the problem states that you can use up to 100 GB maximum, the domain is all real numbers from 0 to 100. In interval notation, this is written as [0, 100].
The range of the function is the set of all possible output values, which in this case is the total cost in dollars of the cell phone plan. The minimum cost is 45 (when 100 GB are used, because 0.25*100 + 20 = 45). So, the range is all real numbers from 20 to 45. In interval notation, this is written as [20, 45].
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