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Worked example: determining domain word problem (real numbers)

Determining the domain of a function that models the height of a plant over time.

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  • leaf blue style avatar for user Z C
    Why integers over real numbers? Well, if the plant height was only measured once a day, integers seems like it would make more sense. We don't have enough information though.

    Also, plants have height even after they die. I think the end point for the interval of the domain should be the day it was discarded.
    (15 votes)
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    • piceratops ultimate style avatar for user Just Keith
      This is obviously a simplification of reality. A real-world modeling function would much more advanced, requiring skills you've not studied yet.

      Plants stop growing when they die, so there is no longer any need to continue modeling their height after that day: whether it is the same, a week or a month after they die, we can just just their final height.
      (19 votes)
  • aqualine ultimate style avatar for user Dshort5698
    ok I'm totally lost. I have no idea how to get the interval of the domain and I've watched these videos multiple times.
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      Look at the example in the video.
      1) It tells you the function is called "h(t)". This tells you that the input value is the variable "t". So, your domain will be based upon the values for "t".
      2) The problem tells you that "t" is the days from the time she bought the plant. This tells you that "t=0" would be the time she bought the plant. This gives you a reference point to work from.
      3) The plant started growing 2 days before she bought it. This tells you that "t" can = -2 (remember, t=0 is when she bought the plant). This is your lowest value for "t".
      4) The problem tells you she had the plant for 98 days after buying it. So, "t" can go up to 98. This is the largest value that "t" can become.
      5) Thus, domain = {-2, 98] and since "t" can be in fractions, you use real number.

      Hope this helps.
      (32 votes)
  • mr pink red style avatar for user Vivian Hir
    How can you decide whether it is an integer or real number? I thought an integer for days would make more sense.
    (11 votes)
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  • leaf blue style avatar for user Smit
    What's the difference between a real number and an integer?
    (7 votes)
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  • duskpin tree style avatar for user Bian Lee
    The question says, "t days from the times she bought it" and so how can the domain include -2, which the time she didn't own the plant yet? Why doesn't it start at 0, from the time she bought it? Also, what are integers and real numbers and why is real number the better choice for the domain?
    (5 votes)
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    • stelly blue style avatar for user Kim Seidel
      The phrase "t days from the time she bought it" would mean that t=0 is when she bought it. It doesn't specify that "t" can't be less than 0.

      The 1st sentence in the problem tells us that the plant spouted (so started growing) 2 days before she bought it. This is where the t = -2 comes from because the plant started growing 2 days before she bought it.

      Integers are numbers like: -5, 0 3, -11, 14, etc. There are no fractions and no decimals.
      Real numbers include integers, but also include all fractions and decimals.

      So, why is the domain real numbers? Because plants grow in fractional units.

      Hope this helps.
      (4 votes)
  • orange juice squid orange style avatar for user gfaignant
    Did anyone else notice that beautiful was spelled wrong in the video?
    (6 votes)
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  • starky ultimate style avatar for user Edy
    What is the difference between parentheses () and brackets []
    (3 votes)
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  • duskpin sapling style avatar for user Chelsea B.
    If the domain set is {-2,28}, why couldn't Sal have selected integers, as the choice to represent the domain? What makes Real numbers the best choice?
    (2 votes)
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  • aqualine ultimate style avatar for user Thejas RS
    Wouldn't Rational numbers be a more appropriate domain for the function? I mean, it is hard to imagine an irrational point on a day.
    (3 votes)
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  • duskpin seed style avatar for user thaakirah.jeter
    How do you know when is the right time to choose whether its an integer or a real number?
    (2 votes)
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    • sneak peak blue style avatar for user Zora Choi
      It depends on the question. For this problem, you choose real number, because the amount of days don't have to be whole numbers. However, if the question is asking the something like the amount of boxes, you choose integers, because the amount of boxes has to be a whole number.
      (1 vote)

Video transcript

Pooja had a beautiful plant. The plant began sprouting 2 days before Pooja bought it, and she had it for 98 days before it died. At its tallest, the plant was 30 centimetres tall. Alright, let h of t denote the height of Pooja's 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? They tell us whether it's integers or real numbers. So we just need to remind ourselves. The domain of a function, that's a set of all the inputs for which the function is defined. And the inputs here, this is 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, in terms of, 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 3.175 days? So I don't see any real -- not any reason why t couldn't be a subset of real numbers. Why you can think about, you know, the 90 -- 97.99 day. So I would say real numbers. And let's see. Define the interval of the domain. So t. Let's see, the t would be defined up to 2 days before she bought the plant. So I would say that t is equal to negative 2, all the way to 98 days. And t could be equal to negative 2. That would be 2 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 2. I would include the low point, so that's why I'm using the bracket. If I wanted t to be greater than, not greater than or equal to, I would do a parentheses. But since t could be equal to negative 2, I'm gonna use the brackets. And at the high end, it's 98, and we're going to include 98. So I'm gonna 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-- t could be negative 2 but -- right I would say negative 2 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.