Question 744604

Relations and functions are very closely related. While all functions are relations, not all relations are functions. That's because functions are a special subset of relations. 

For a relation to be a function, there must be {{{one}}} and {{{only}}}{{{ one}}}{{{ y}}} value for {{{each}}}{{{ x}}} value. 

If there are two pairs of numbers that have the {{{same}}}{{{ x}}} value but {{{different}}}{{{ y}}} values, then the relation is {{{NOT}}} a function.
 
A.({{{2}}},{{{ 6}}}), ({{{3}}},{{{ 9}}}), ({{{4}}}, {{{2}}}), ({{{3}}}, {{{6}}}) 


since pairs ({{{3}}},{{{ 9}}}) and ({{{3}}}, {{{6}}}) have the {{{same}}}{{{ x}}} value but {{{different}}}{{{ y}}} values, the relation is {{{NOT}}} a function


B.({{{2}}},{{{ 8}}}), ({{{3}}}, {{{6}}}), ({{{2}}}, {{{4}}}), ({{{0}}}, {{{2}}})

({{{2}}},{{{ 8}}}), ({{{3}}},{{{ 6}}}), ({{{2}}}, {{{4}}}), ({{{0}}}, {{{2}}}) 

since pairs ({{{2}}},{{{ 8}}}) and ({{{2}}},{{{ 4}}}) have the {{{same}}}{{{ x}}} value but {{{different}}}{{{ y}}} values, the relation is {{{NOT}}} a function


C.({{{3}}},{{{ -2}}}), ({{{4}}},{{{ 7}}}), ({{{-2}}}, {{{5}}}), ({{{-4}}}, {{{5}}})

since this relation has NO pairs that have the {{{same}}}{{{ x}}} value but {{{different}}}{{{ y}}} values, the relation {{{IS}}} a function

D.({{{4}}}, {{{7}}}), ({{{-2}}}, {{{5}}}), ({{{1}}}, {{{3}}}), ({{{-2}}}, {{{1}}})

since pairs ({{{-2}}},{{{ 5}}}) and ({{{-2}}},{{{ 1}}}) have the {{{same}}}{{{ x}}} value but {{{different}}}{{{ y}}} values, the relation is {{{NOT}}} a function


so, your answer is : {{{C}}}