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Which of these tables make $y$ a function of $x\text{?}$

$x$

$y$

$2$

$1$

$3$

$1$

$4$

$2$

$5$

$2$

$6$

$2$

This table make $y$ a function of $x\text{.}$

$x$

$y$

$8$

$3$

$9$

$2$

$5$

$1$

$2$

$0$

$8$

$1$

This table make $y$ a function of $x\text{.}$

$x$

$y$

$5$

$9$

$5$

$9$

$6$

$2$

$6$

$2$

$6$

$2$

This table make $y$ a function of $x\text{.}$

Solution

This table does make $y$ a function of $x\text{.}$ In the table, no $x$ -value is repeated.

This table does not make $y$ a function of $x\text{.}$ In the table, the $x$ -value $8$ is repeated and it is paired with two different $y$ -values, $3$ and $1\text{.}$

This table does make $y$ a function of $x\text{,}$ but you have to think carefully. It’s true that the $x$ -value $5$ is used more than once in the table. But in both places, the $y$ -value is the same, $9\text{.}$ So there is no conceptual issue with asking for $f(5)\text{;}$ it would definitely be $9\text{.}$ Similarly, the repeated use of $6$ as an $x$ -value is not a problem since it is always paired with output $2\text{.}$