Question 1151304
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Problem
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To celebrate his birth, Damien's parents planted a tree in their yard. The tree's growth each year, in feet, can be modeled by the equation f(x)=2.5x+4. The tree is expected to reach full height when Damien is 18 years old. Interpret the values in the function to answer the given questions.
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<font color=blue>What was the height of the tree in feet when it was planted?</font>
Answer: 4 feet


To get this answer, plug in x = 0.
f(x) = 2.5*x + 4
f(0) = 2.5*0 + 4
f(0) = 0 + 4
f(0) = 4
The input x = 0 leads to y = f(x) = 4.

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<font color=blue>How tall will with tree be in feet when Damien is 18 years old?</font>


Answer: 49 feet


Now plug in x = 18
f(x) = 2.5*x + 4
f(18) = 2.5*18 + 4
f(18) = 45 + 4
f(18) = 49

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<font color=blue>What is the domain for the function?</font>


The domain is the set of real numbers x such that {{{0 <= x <= 18}}}. Which can be described as "the set of numbers between 0 and 18 inclusive of both endpoints". We stop at x = 18 because the tree reaches its full height at this point. We have x = 0 as the lower boundary because negative year values do not make sense.


The domain in interval notation is [0, 18]. The square brackets tell the reader "include the endpoints".
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<font color=blue>What is the range for the function?</font>


The range is a similar story: The range is {{{0 <= y <= 49}}} which in interval notation would be [0, 49]. The smallest the tree can get is 0 ft, and the largest it can be is 49 feet.
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