Question

(a) the relationship between the $x$ and $y$ values in this table is not a function. one of the values of $x$ is missing from the table, as shown.

$x$	7	12	?

what is one value of $x$ that could replace the missing value in the table to show that $y$ is not a function of $x$?

Explanation:

Step1: Recall function definition

A function requires each $x$-value to map to exactly one $y$-value. For the relationship to NOT be a function, an $x$-value must map to more than one $y$-value.

Step2: Identify existing $x$-values

The table already has $x = 7$ (paired with $y=-6$) and $x = 12$ (paired with $y=-1$).

Step3: Choose duplicate $x$-value

If we reuse an existing $x$-value, that $x$ will now correspond to two different $y$-values, violating the function rule. For example, using $x=7$ will pair it with both $y=-6$ and $y=8$.

Answer:

$7$ (or $12$, either is a valid answer)