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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)?\newlineChoices:\newline(A)all real numbers from 00 to 7272\newline(B)all whole numbers greater than or equal to 7272\newline(C)all real numbers from 00 to 12°F12\degree\text{F}00\newline(D)all whole numbers less than or equal 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)?\newlineChoices:\newline(A)all real numbers from 00 to 7272\newline(B)all whole numbers greater than or equal to 7272\newline(C)all real numbers from 00 to 12°F12\degree\text{F}00\newline(D)all whole numbers less than or equal to 12°F12\degree\text{F}11
  1. Define Function Domain: 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 begins his day by turning on the oven and the temperature rises steadily for an hour, we need to consider the time from when he turned it on until it reached its ideal temperature.
  2. Calculate Time Interval: An hour has 6060 minutes. Since the temperature reaches its ideal temperature after an hour, the domain of T(m)T(m) includes all the minutes from the time Stefan turned on the oven until 6060 minutes later. This means the domain is from 00 to 6060 minutes.
  3. Consider All Real Numbers: The domain includes all real numbers from 00 to 6060 because the temperature can be measured at any fraction of a minute within this interval. Therefore, the domain is not limited to whole numbers or integers.

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