1. The problem asks us to determine which value of $a$ makes the given relation a function. 2. A relation is a function if every input (first element of each ordered pair) corresponds to exactly one output (second element). 3. The given relation is $\{(-2,3), (a,4), (1,9), (0,7)\}$. 4. We need to check if any choice for $a$ causes the input values to repeat, which would violate the definition of a function. 5. The current inputs are $-2$, $a$, $1$, and $0$. 6. The inputs $-2$, $1$, and $0$ are distinct. 7. We test each choice: - a) $a=1$: inputs would be $-2$, $1$, $1$, $0$; input $1$ repeats, so not a function. - b) $a=-2$: inputs would be $-2$, $-2$, $1$, $0$; input $-2$ repeats, so not a function. - c) $a=0$: inputs would be $-2$, $0$, $1$, $0$; input $0$ repeats, so not a function. - d) $a=4$: inputs would be $-2$, $4$, $1$, $0$; all distinct, so this is a function. 8. Therefore, the replacement for $a$ that makes the relation a function is $\boxed{4}$.