Final answer:
The area function of the rectangular plot is y = 300x - x², with a domain for x as all real numbers between 0 and 300, exclusive.
Step-by-step explanation:
To solve the problem of finding the function for the area of the rectangular plot (y) in terms of one of its dimensions (x), given that 600m of fencing is required to enclose it, we can set up two equations based on the information provided.
The perimeter of the rectangle is given by the formula 2x + 2w = 600, where w is the width of the rectangle, and x is one of the given dimensions. We can solve for w to get w = (600 - 2x)/2, which simplifies to w = 300 - x.
The area of the rectangle (y) can be expressed as x multiplied by w, or y = x(300 - x). This simplifies to y = 300x - x². The domain of this function represents all possible values of x that can form a valid rectangle. Since a rectangle cannot have a negative or zero length, the domain is all real numbers such that 0 < x < 300.