Relations and Functions Intermediate Algebra II Section 2.1

Example 1 Relation  { (-4, 3), (-1, 7), (0, 3), (2, 5)} Domain  { -4, -1, 0, 2 } Range  { 3, 7, 5 }

Example 2 Relation  { (-2, 2), (5, 17), (3, 3), (5, 1), (1, 1), (7, 2) } Domain  { -2, 5, 3, 1, 7 } Range  { 2, 17, 3, 1 }

Definitions Relation  A set of ordered pairs. Domain  The set of all inputs (x-values) of a relation. Range  The set of all outputs (y-values) of a relation.

Example Relation  {(1, 0), (5, 2), (7, 2), (-1, 11)} Domain  {1, 5, 7, -1} Range  {0, 2, 11}

Definition Function  A relation in which each input ( x value) maps to exactly one output (y value).

Are these functions? { (0, 2), (1, 0), (2, 6), (8, 12) } { (0, 2), (1, 0), (2, 6), (8, 12), (9, 6) } { (3, 2), (1, 0), (2, 6), (8, 12), (3, 5), } { (3, 2), (1, 2), (2, 2), (8, 2), (7, 2) } { (1, 1), (1, 2), (1, 5), (1, -3), (1, -5) }

Function Operations f(x) = -2x + 1 Find f(3)f(3) = -2(3) + 1 f(3) = f(3) = -5 Find f(-5)f(-5) = -2(-5) + 1 f(-5) = f(-5) = 11 (3, -5) (-5, 11)