The set of abscissas (the first components) of the ordered pairs in a relation.

The domain of a relation is the set of values of the independent variable for which a relation is defined.

The domain can be determined graphically by imagining a vertical line moving right or left over the graph of the relation.

Where the vertical line intersects the graph of the relation, an x-value which is part of the domain of the function occurs.

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

State the domain 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

State the domain of each of the following relations.

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

Domain of A: { -2, 1, 2, 3 )

Relation p: p(x) = x² - 2x - 3

Domain of p: { x | x ∈ R }

Since any real number substituted into the function g(x) results in another real number, the domain of g(x) is the real numbers.

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

Domain of H: { x | x ≤ -2, x ≥ 2 }

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

Domain of E: { x | -4 ≤ x ≤ 4 }

Relation R: xy = 1

Domain of R: { x | x ≠ 0 }