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Precalculus: Functions

Problems

Sets and Relations

Functions

Problem : Let set A = {1, 2, 3} and set B = {4, 5} . What is their Cartesian product A×B ?

A×B = {(1, 4),(1, 5),(2, 4),(2, 5),(3, 4),(3, 5)} . This is every possible ordered pair from which the first element is taken from A and the second element taken from B .

Problem : What is the Cartesian product of the set of real numbers and itself?

The Cartesian product is every ordered pair in the coordinate plane.

Problem : What is the Cartesian product of the set of positive real numbers with itself?

The Cartesian product is every ordered pair in the first quadrant of the coordinate plane.

Problem : What is the domain and range of the relation {(2, 4),(4, 8),(8, 16)} ?

Domain D = {2, 4, 8} . Range R = {4, 8, 16} .

Problem : What is the domain and range of the relation y = ± ?

Domain D is real numbers > 0 . Range R is all real numbers.

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