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pooja had a beautiful plant the plant began sprouting two days before pooja bought it and she had it for 98 days before it died at its tallest the plant was 30 centimeters tall all right let H of T denote the height of poojas plant H measured in centimeters T days from the time she bought it which number type is more appropriate for the domain of the function and they tell us whether it's integers or real numbers so we just have to remind ourselves the domain of a function that's the set of all the inputs for which the function is defined and the inputs here these are T and it represents days and if I input T the number of days into the function H it'll output the height of the plant so let's think about it at first you might say think in terms of you know 0 days 1 days 2 days and you might be tempted to say integers but why not think about one and a half days or three point one seven five days so I don't see any root not any reason why T couldn't be a subset of real numbers why you can think about you know the the ninety ninety seven point nine ninth day so I would say real numbers and I say defined the interval of the domain so T let's see the the T would be defined up to two days before she bought the plant so I would say that's T is equal to negative two all the way to ninety eight days and T could be equal to negative two that would be two days before she bought it or as high as 98 so let's think about it so the interval I would include I would include negative two I would include the the low point so that's why I'm using the brackets if I wanted T to be greater than not greater than or equal to I would do the parenthesis but since T could be equal to negative two I'm gonna use the brackets and at the high end it's 98 and we're going to include 98 so I'm going to put the brackets there as well so T would be a member of real numbers such that it is a member of this of this interval right over here so negative T could be T could be negative two but okay I guess you say negative two is going to be less than or equal to t which is going to be less than or equal to 98 let's check our answer got it right