Answer:
1) [tex]y=\frac{4}{5}*\sqrt{x}[/tex] 2) Check below
Step-by-step explanation:
f(x) = Total length of a row of bookshelves
1) The Warehouse is a square, and Isabel takes 100ft² or in case She takes up to the whole 8100 ft² area, as it's another square. Then its lenghts are congruent and equal to 10 ft or to 90ft. Then
x=100 [tex]A_{square} =100\\ \sqrt{100} = \sqrt{l^{2}}\\ 10=l[/tex] or
x=8100 [tex]A_{square} =8100\\ \sqrt{8100} = \sqrt{l^{2}}\\ 90=l[/tex]
y or f(x)= total length of a row of bookshelves
Modelling the function:
[tex]y=\frac{4}{5}*\sqrt{x}[/tex]
[tex]y=\frac{4}{5}*\sqrt{100}[/tex]
[tex]y=\frac{4}{5}*\sqrt{8100}[/tex]
x | y
100 | 8
(...) | (...)
8100 | 72
So the Domain = [100, 8100] and the Range [8, 72]
According to this function for an area of 100 ft², the length of bookshelves are 8 ft. Until 72 feet for an area of 8100 ft²
100 ≤ x ≤ 8100 and therefore 8 ≤ y ≤ 72
2) Function graphed below. Notice that it fits either value for x as, x fits for the area. And the Domain and the Range well defined.
