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Stefan works as a pizza chef. He begins his day by preheating the pizza oven. Today, the oven's interior temperature was 72°F72\degree\text{F} when Stefan turned it on high-power to preheat. The temperature rose steadily at a rate of 12°F12\degree\text{F} per minute until it reached its ideal temperature an hour later. Then, Stefan reduced the power so the temperature would stop rising. The function T(m)T(m) represents the oven's interior temperature, in °F\degree\text{F}, after mm minutes of preheating.\newlineWhat is the domain of T(m)T(m)?\newline(A) all whole numbers greater than or equal to 7272\newline(B) all real numbers from 00 to 7272\newline(C) all whole numbers less than or equal to 1212\newline(D) all real numbers from 00 to 12°F12\degree\text{F}11

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Q. Stefan works as a pizza chef. He begins his day by preheating the pizza oven. Today, the oven's interior temperature was 72°F72\degree\text{F} when Stefan turned it on high-power to preheat. The temperature rose steadily at a rate of 12°F12\degree\text{F} per minute until it reached its ideal temperature an hour later. Then, Stefan reduced the power so the temperature would stop rising. The function T(m)T(m) represents the oven's interior temperature, in °F\degree\text{F}, after mm minutes of preheating.\newlineWhat is the domain of T(m)T(m)?\newline(A) all whole numbers greater than or equal to 7272\newline(B) all real numbers from 00 to 7272\newline(C) all whole numbers less than or equal to 1212\newline(D) all real numbers from 00 to 12°F12\degree\text{F}11
  1. Convert hours to minutes: The domain of a function is the set of all possible input values (independent variable) which, in this case, is the time in minutes, mm, that the oven has been preheating. Since Stefan preheated the oven for an hour, we need to convert this hour into minutes to find the upper limit of the domain.\newline11 hour = 6060 minutes.
  2. Define domain interval: The oven starts preheating from time m=0m = 0 minutes and continues until m=60m = 60 minutes. Therefore, the domain of T(m)T(m) includes all real numbers from 00 to 6060, as the temperature is changing continuously and steadily over this interval.
  3. Limit domain to preheating duration: The domain does not include any times before 00 minutes or after 6060 minutes, as the oven was not preheating before Stefan turned it on and stopped rising in temperature after 6060 minutes. Therefore, the domain is limited to the duration of the preheating period.

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