Rachel

Problem:

Solution:

(a)

The length of the box would be $ (12 - 2s) $
The width of the box would be $ (10 - 2s) $
The height of the box would be $ s $

The volume would be $ f (s) = s(10 - 2s)(12 - 2s) $

(b)

No, we cannot, look at the plot, we can see that there are two ways we can achieve volume = 80, that make it impossible for us to define a 'function' because one input must lead to one output but we have two.

(c)

The domain of f is (0, 5), because you have to cut some square, and you cannot cut more than or equals to 5 x 5 (that would cut the whole width ... )