Bronze is the alloy or mixture of metals copper and tin. Properties of bronze depend on percentage of copper in mix. A chemist makes decision to study properties of the given alloy of bronze as proportion of copper is differed. She begins with 9kg of bronze which contain 3 kg of copper and 6kg of tin and either adds or removes copper. Let ƒ(x) be percentage of copper in mix if x of kg are added (x>0) or removed (x<0).
a) Express domain and range of ƒ. What does the answer mean on context of bronze?
b) Determine formula in terms of x for ƒ(x).
c) If formula you found in part b was not intended to represent percentage of copper in the alloy of bronze, but instead simply defined the abstract mathematical function, what would be domain and range of the function?