A relation $f$ from a set $A$ to a set $B$ is said to be a function if every element of set $A$ has one and only one image in set $B$. This means that no two distinct ordered pairs in $f$ can have the same first element.

To determine if $f = \{(ab, a + b) : a, b \in Z\}$ is a function, we must check if a specific first element corresponds to a unique second element. Let us consider specific integer values for $a$ and $b$.

For $a = 2$ and $b = 3$, the ordered pair is $(ab, a + b) = (6, 5)$. For $a = 1$ and $b = 6$, the ordered pair is $(ab, a + b) = (6, 7)$. In this case, the same first element, $6$, is associated with two different second elements, $5$ and $7$. Since the element $6$ has more than one image, the relation $f$ is not a function from $Z$ to $Z$.