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6 2.1 Functions and Their Graphs RECALL: coordinate plane – cartesian plane or x-y plane ordered pairs – points in the form (x, y) x-coordinate – first value in an ordered pair. y-coordinate – the second value in an ordered pair. 4 2 -5 5 -2 Identify the quadrants -4 Function Graphing Activity -6 1.) Can you identify a difference between the graphs that are functions and the graphs that are NOT function? If so, what is it? Method 1: Method 2: 2.) Using either method 1 or method 2 decide which of the following graphs are functions? Please explain your answer. ________________________ ________________________ ___________________ ________________________ ________________________ ___________________ Definitions for Review domain – the set of all possible x-values or the input What are some of the values in the domain for graph? 6 4 range – the set of all possible y-values or the output What are some of the values in the range for the graph? 2 -5 5 -2 function – a set of ordered pairs for which there is exactly one y-value for each x-value. For the following sets of ordered pairs answer questions below: a.) Do the ordered pairs graph a function?(Method 1?) b.) Using method 2, explain why the set of ordered pairs is or is not a function? c.) What is the domain and range? EX: 1 6 4 (−3, 3) (1, −2) 2 (4,1) (1, 4) -5 5 -2 -4 -6 EX: 2 6 4 (−3,3) (1,1) (3,1) (4, −2) 2 -5 5 -2 -4 -6 Evaluating Functions Evaluate the following functions for the given input. f ( x) = 3x 2 − 2 x + 7 f (−2) g ( x) = 4 x + 1 g(7) Real Life Example BALLOONING In March of 1999, Bertrand Piccard and Brian Jones attempted to become the first people to fly around the world in a balloon. Based on an average speed of 97.8 kilometers per hour, the distance d (in kilometers) that they traveled can be modeled by d = 97.8t where t is the time (in hours). They traveled a total of about 478 hours. The rules governing the record state that the minimum distance covered must be at least 26,700 kilometers. a. Identify the domain and range and determine whether Piccard and Jones set the record. b. Graph the function. Then use the graph to approximate how long it took them to travel 20,000 kilometers. 6 4 2 5 Homework: p. 71-73 # 19-23, 30-33, 43-48, 55-58