A simple corollary of Theorem MR: If $f(x)=f_1(x)\cdot f_2(x) =0$ then either $f_1(x)=0$ or $f_2(x) =0$.

For an elementary function, $f$ that can be expressed in a form with the final step in its definition being the product of two elementary functions, $f_1$ and $f_2$, the corollary entails further that set of the roots of $f$ is the union of the set of roots of the simpler elementary functions, $f_1$ and $f_2$.

A mapping diagram can visualize these results by visually connecting roots in mapping diagrams for $f_1$ and $f_2$ to a root of $f$.

The relation of quotients to roots is given by the simple but important theorem that is a result of other basic field properties of real numbers.

For an elementary function, $f$ that can be expressed in a form with the final step in its definition being the quotient of two elementary functions, $f_1$ and $f_2$, the corollary entails further that set of the roots of $f$ is the set of roots of the function, $f_1$.

Example AEF.DR.1