Determine which of the following relations is a function. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 10, negative 5, 0, 5, 10. Column 2 is labeled y with entries 10, 5, 0, negative 5, negative 10. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 3, negative 1, 0, 0, 3. Column 2 is labeled y with entries 2, 1, 2, 1, 4. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 8, negative 2, 1, 2, 4. Column 2 is labeled y with entries negative 4, negative 2, 3, 4, 6. A 2-column table with 5 rows. Column 1 is labeled x with entries 0, 1, 2, 2, 5. Column 2 is labeled y with entries 2, 4, 2, 6, 7.

[tex](A)\begin{tabular}{cc}\\x & y\\\hrule\\-10 &10\\-5& 5\\0&0\\5&-5\\10&-10\end{tabular}\\(B)\begin{tabular}{cc}\\x&y\\ \hrule\\-3&2\\-1&1\\0&2\\0&1\\3&4\end{tabular}\\(C)\begin{tabular}{cc}\\x&y\\\hrule\\-8&-4\\-2&-2\\1&3\\2&4\\4&6\end{tabular}\\(D)\begin{tabular}{cc}\\x&y\\\hrule\\0&2\\1&4\\2&2\\2&6\\5&7\end{tabular}[/tex]

Relations (A) and (C) are functions.

What is a function?

A relation from set A to a set B is a function if every element of set A has a unique image in set B.

Explanation

In relation A, all the five elements under column x have assigned one and only one element in y. So, according to the definition, A is a function.

In relation B, the element 0 has two image in y, viz 2 and 1. So, the element 0 in x doesn't has a unique image in y. The relation B is, thus, not a function.

In relation C, each element in the set x has a unique image in y. So, C qualifies as a function.

In relation D, again the element 2 doesn't has a unique image in set y. So, D is not a function.

The relations A and C are functions.

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