Combine standard function types arithmetically to create models.
Form and interpret the product of two functions in context
Problem
A rectangle's width and length are \(w(x)=x+3\) and \(l(x)=x+8~\text{units}\). Form its area as the product function \(A(x)=(w\cdot~l)(x)\), substitute the two factors, expand as a check, and interpret the output units.
Big Picture
What this problem is really about
The product function multiplies both side-length outputs at the same input, matching the rectangle area relationship. We’ll substitute the dimension rules as factors, expand to check every cross term, and use length times length to interpret the result in square units.
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