A $12 \mathrm{~kg}$ Sample of a Certain Alloy (Mixture of Metals) Contains

Multiple Choice

A $12 \mathrm{~kg}$ sample of a certain alloy (mixture of metals) contains $2 \mathrm{~kg}$ of tin and $10 \mathrm{~kg}$ of copper. A chemist decides to study the properties of the alloy as its percentage of tin is varied. Suppose $x$ represents the quantity of tin, in $\mathrm{kg}$ , the chemist adds to the sample. Let $f(x)$ represent the fraction of the mixture's mass composed of tin--that is, the ratio of the tin's mass to the mixture's total mass. A negative value of $x$ represents a quantity of tin removed from the original $12 \mathrm{~kg}$ sample. What is the domain of $f$ ?

A) All real numbers $x$ .
B) All $x \geq 0$ .
C) All $x \geq 2$ .
D) All $x \geq-2$ .
E) All $x \geq-12$ .