Question

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.)

Answer 1

Answer is in ss, btw press "Help Me Solve This" and exit out to quickly get a new question!

Answer 2

(a)
`l = -w + 21`

(b) Domain:
`0 <w < 21` (See attachment for graph)

(c)
`f(w) = -w + 21`

Explanation:

Given

`2(l + w) = 42`

`l = length`

`w = width`

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

All we need to do is make l the subject in
`2(l + w) = 42`

Divide through by 2

`l + w = 21`

Subtract w from both sides

`l + w - w = 21 - w`

`l = 21 - w`

Reorder

`l = -w + 21`

Solving (b): The graph

In (a), we have:

`l = -w + 21`

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
`0 <w < 21`

--------------------------------------------------------------------------------------------------

To check this

When
`w = 1`

`l = -1 + 21`

`l = 20`

`(w,l) = (1,20)`

When
`w = 20`

`l = -20 + 21`

`l = 1`

`(w,l)= (20,1)`

--------------------------------------------------------------------------------------------------

See attachment for graph

Solving (c): Write l as a function
`f(w)`

In (a), we have:

`l = -w + 21`

Writing l as a function, we have:

`l = f(w)`

Substitute
`f(w)` for l in
`l = -w + 21`

`l = -w + 21` becomes

`f(w) = -w + 21`