How do you find the domain and range and determine whether the relation is a function given {(-2,5), (3,7), (-2,8)}?

1 Answer
martin23239
Feb 9, 2018

\qquad \qquad \mbox{Domain} = { -2, -3,-2 }.

\qquad \qquad \mbox{Range} \quad = { 5, 7, 8 }.

\qquad \qquad \mbox{Relation is a Function.}

Explanation:

\mbox{Given Set of Ordered Pairs =} \quad { (-2,5), (-3,7), (-2,8) }

\mbox{Domain = Set of First Coordinates} \quad = \qquad \quad \ { -2, -3,-2 }

\quad \mbox{(removing duplicate entries within a set)} \qquad = \quad { -2, -3}.

\mbox{Range = Set of Second Coordinates} \quad = \qquad \quad \ { 5, 7, 8 }.

\mbox{A Relation is a Function precisely when there are no repeated} \ \ \mbox{first coordinates. Scanning the first coordinates of the Relation,} \ \mbox{we see that the first coordinate -2 is repeated !!} \ \mbox{So the Relation is not a Function.}

\

\mbox{Summary:}

\qquad \qquad \mbox{Domain} = { -2, -3,-2 }.

\qquad \qquad \mbox{Range} \quad = { 5, 7, 8 }.

\qquad \qquad \mbox{Relation is a Function.}

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