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Do Now Use the graph paper and the ruler to make a set of axes and graph the points: A (1,4) B ( – 2,3) C (4, – 5) D (– 5, – 3) E (3,1) Do you remember how to label the quadrants? Graphing & Quadrants Review y Quadrant II Quadrant I X is – X is + and Y is + and Y is + x Quadrant III Quadrant IV X is – and Y is – X is + and Y is – Notes On Graphing Points are located on the coordinate plane. Points are also called ordered pairs. (x, y) The x-coordinate tells you how many units to move right/left. The y-coordinate tells you how many units to move up/down. RELATIONS A relation is a set of ordered pairs. Ways to represent a relation: ORDERED PAIRS •(3,4) •(-2,8) •(-4,-9) TABLE X 3 -2 -4 Y 4 8 -9 MAPPING X Y 3 -2 -4 4 8 -9 OR YOU CAN GRAPH THE POINTS Example – Ken Griffey, Jr.’s home run and strikeout numbers can be summarized as follows for the years 1994 – 2001. (HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121), (56, 121), (48, 108), (40, 117), (22, 72). Show this relation as a table, graph and mapping. Home Runs StrikeOuts 40 73 17 53 49 104 56 121 56 121 48 108 40 117 22 72 (HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121), (56, 121), (48, 108), (40, 117), (22, 72). 140 Graph: 120 100 80 60 40 20 -100 -50 50 -20 100 (HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121), (56, 121), (48, 108), (40, 117), (22, 72). Mapping: 40 73 17 53 49 104 56 121 56 121 48 108 40 117 22 72 Domain & Range The domain of a relation is the set of all x – values. The range of a relation is the set of all yvalues. (Remember they’re in alphabetical order) a. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a table, a graph, and a mapping. Answer: x y 3 4 5 –2 6 2 –1 3 b. Determine the domain and range. Answer: D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6} JUST SWITCH THE COORDINATES IN EACH PAIR EXAMPLES: Find the inverse of each relation. Then state the domain and range of each inverse. 1) (-9,5) (3,-7) 2) X -9 4 Y 7 8 (-5,-6) (3,7) 3. -3 -5 8 4 7 4 -3 5 Express the relation shown in the mapping as a set of ordered pairs. Then write the inverse of the relation. Answer: Relation: {(3, 2), (–4, 1), (5, 2)} Inverse: {(2, 3), (1, –4), (2, 5)}