Mathematical Models (PreCalc)

These are a few review problems I was given for a upcoming test and I'm completely stumped how to do these.

My main problem is the concept of "Expressing :blank: as a function of :blank:".

You can answer the problems completely if you'd like ( learning for my self would benefit me more but I could always do other problems ) but I just need a very dumbed down explanation.

Example 1)

The demand for a certain commodity is given that is, x units of the commodity well be demanded by consumers when the price is dollars pre unit. Total consumer expenditure is the amount of money consumers pay to buy x units of the commodity.

A: Express consumer expenditure as a function of x, and sketch the graph of .

B: Use the in part A to determine the level of production x at which consumer expenditure is largest. What price corresponds to maximum consumer expenditure?

Example 2)

A spherical cell of radius r has volume

and surface are .

Express V as a function of S. If S is doubled, what happens to V?

Thanks for any help any one gives.