2.1: Relations and Functions 2.2: Linear Equations 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, independent variable Domain: {-3, -2, 0, 1, 2 } Range - the set of all outputs of a function, y-coordinates, dependent variable 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 (YOU) Range (BIRTHDAY) 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? If so, describe the domain and range 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). What is Slope?? Slope y vertical change (rise) y2 y1 slope x horizontal change (run) x2 x1 Ex4) 2, 2 and 4,2 Ex5) 2,7 and 8, 6 Slope (cont.) y (rise) slope x(run) What does it mean if the slope is zero? What does it mean if the slope is Undefined? 2.1: Relations and Functions 2.2: Linear Equations Homework #9: Pg 59 #1-29 odd Pg 67 #11-19 odd