Katrina buys a 42-ft roll of fencing to make a rectangular play area for her dogs. Use 2({ + w)= 42 to write a function for the length, given the width. Graph the
function. What is a reasonable domain for the situation? Explain.

The function f(w) = gives the length as a function of the width.
(Simplify your answer.)

(a)

(b) Domain: (See attachment for graph)

(c)

Step-by-step explanation:

Given

Solving (a): A function; l in terms of w

All we need to do is make l the subject in

Divide through by 2

Subtract w from both sides

Reorder

Solving (b): The graph

In (a), we have:

Since l and w are the dimensions of the fence, they can't be less than 1

So, the domain of the function can be

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To check this

When

When

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See attachment for graph

Solving (c): Write l as a function

In (a), we have:

Writing l as a function, we have:

Substitute for l in

becomes