Range
Definition

The set of ordinates (the second components) of the ordered pairs in a relation.

The range of a relation is the set of values of the dependent variable for which a relation is defined.


The range can be determined graphically by imagining a horizontal line moving up or down over the graph of the relation.


Where the horizontal line intersects the graph of the relation, a y-value which is part of the range of the function occurs.


Where the horizontal line does NOT intersect the graph of the relation, a y-value occurs (based on the vertical position of the horizontal line) which is NOT part of the range of the function.


Examples

State the range of each of the following relations.


Relation A: { ( -2, -3 ), ( 1, 5 ), ( 2, -4 ), ( 2, 5 ), ( 3, 3 ) }

Relation p: p(x) = x2 - 2x - 3

Relation H: { ( x, y ) | x2 - y2 = 4 )

Relation E: { ( x, y ) | x2 + 4y2 = 4 )

Relation R: xy = 1


Solutions

State the range of each of the following relations.


Relation A: { ( -2, -3 ), ( 1, 5 ), ( 2, -4 ), ( 2, 5 ), ( 3, 3 ) }

Range of A: { -4, -3, 3, 5 )


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Relation p: p(x) = x2 - 2x - 3

Range of p: { y | y ≥ -4 }


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Relation H: { ( x, y ) | x2 - y2 = 4 )

Range of H: { y | y ∈ R }


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Relation E: { ( x, y ) |x2 + 4y2 = 16 )

Range of E: { x | -2 ≤ x ≤ 2 }


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Relation R: xy = 1

Range of R: { x | x ≠ 0 }


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