SOLUTION: Shelly has 32 m of fencing to make a rectangular pen for her rabbits. The wall of her house will serve as one side of the pen so she will use fencing for only three sides of the re

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Question 1190774: Shelly has 32 m of fencing to make a rectangular pen for her rabbits. The wall of her house will serve as one side of the pen so she will use fencing for only three sides of the rectangle Express the area of the rabbit pen as a function of its width and then determine the domain and range of the area function.
thanking you in advance )

Answer by ikleyn(52817) About Me  (Show Source):
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Shelly has 32 m of fencing to make a rectangular pen for her rabbits.
The wall of her house will serve as one side of the pen so she will use fencing
for only three sides of the rectangle Express the area of the rabbit pen as a function
of its width and then determine the domain and range of the area function.
thanking you in advance )
~~~~~~~~~~~~~~~~~~~

Let x be the width of the pen.  In other words, x is the dimension of the side
perpendicular to the wall ot the hous.


The fence has three straight line parts: two of them of the length x are perpendicular
to the wall of the house, and the third line is parallel to the wall of the house.


The length of the parallel side is  32-2x meters.


The area of the pen is the prodict of its dimension

     area = a(x) = x*(32-2x) = -2x^2 + 32x.


This quadratic functiom makes sense, when both dimensions are non-negative, i.e.

     x >= 0,  32-2x >= 0,  or  x =< 16.


Thus the domain of this area function is the set of real numbers  0 <= x <= 16.

Solved and explained.