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
Feb 9, 2018

Answer:

# \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.} #