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2.1: Relations and Functions Perfection is a road, not a destination. Every time you live, you get an education. Relation 5 Ex1) Graph the coordinate points: 4 3 (–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2) 2 1 -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 -5 A relation is a set of pairs of input (x) and output (y) values. Written: {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}. 5 Relation {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)} Domain – the set of all inputs of a function (x-coordinates) Domain: {-3, -2, 0, 1, 2 } Range - the set of all outputs of a function (y-coordinates) Range: { -2, 2, 3, 4 } Relation Ex2) Write the ordered pairs for the relation. Find the domain and range. Mapping Diagrams Ex3) {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}. Domain Range Functions A function is a relation in which each input value is paired with only one output value. Domain Range Domain 2 -2 -1 0 3 5 4 Function? 3 4 7 Function? Range 5 6 8 Vertical Line Test Vertical Line Test: If a vertical line passes through at least two points on the graph, the relation is not a function. Ex4) {(-2, -1), (0, 3), (-2, 3), (5, 4)} 6 Ex5) {(3, 6), (2, 6), (7, 8), (4, 5)} 9 5 8 4 7 3 2 6 1 -6 -5 -4 -3 -2 -1 -1 -2 -3 5 1 2 3 4 5 6 4 3 2 -4 -5 -6 1 1 2 3 4 5 6 7 8 9 Vertical Line Test Ex6) Are these relations functions? 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 -1 -1 -1 -2 -2 -2 -3 -3 -3 -4 -4 -4 -5 -5 -5 2 3 4 5 Function Notation Function notation f ( x) is read "f of x" or "a function f of x." y x 2 3 f ( x) x 2 3 Ex7) For the function f ( x) above, find f (2) and f (3). Function Notation Ex8) The surface area of a cube is a function of the length of a side of the cube. Write a function for the surface area of the cube. Find the surface area of the cube with a side 2 inches long. 2.1: Relations and Functions HW: 7, 12, 13, 17, 20, 21, 23, 25, 33, 37, 39, 41, 46, 47 Perfection is a road, not a destination. Every time you live, you get an education.