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## Determining the domain of a function

# Worked example: determining domain word problem (real numbers)

CCSS.Math:

## 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.