Example 1

If $f$ is a mapping of $A$ into $B$, the function $f$ is equal to the function $x \to f(x)$ ($x \in A$, $f(x) \in B$), which is written simply as $x \to f(x)$ or also $(f_x)_{x \in A}$ (the latter notation is especially associated with the phrase “family of elements” instead of “function”).