## Precalculus: Mathematics for Calculus, 7th Edition

The answer to the missing gap is 'one'. Only table $(ii)$ defines $y$ as a function of $x$.
A function $f$ is a tule that assigns to each element $x$ in a set $A$ exactly one element(s) called $f(x)$ in a set $B$. Table $(i)$ does define $y$ as a function of $x$ because each element of $x$ has exactly one element in $y$ which can also be called $f(x)$. Table $(ii)$ does not define $y$ as a function of $x$ because $f(1)=5$ and $f(1)=7$ hence not every element in $x$ has exactly one element in $f(x)$; in this case the element 1 in a set $A$ is assigned to two elements in a set $B$.