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Name _______________________________________ Date __________________ Class __________________ LESSON 3-2 Understanding Relations and Functions Practice and Problem Solving: C Graph each relation. Then explain whether it is a function or not. 1. {(1, 2), (2, 2), (3, 3), (4, 3)} 2. {(1, 5), (2, 4), (3, 5), (3, 4), (4, 4), (5, 5)} _______________________________________ ________________________________________ _______________________________________ ________________________________________ Solve. 3. Locate 5 points on the first graph so that it shows a function. Then change one number in one of the ordered pairs. Locate the new set of points on the second graph to show a relation that is not a function. Explain your strategy. ________________________________________________________________________________________ 4. Identify whether the graph shows a function or a relation that is not a function. Explain your reasoning. ________________________________________________________________________________________ 5. The function INT(x) is used in spreadsheet programs. INT(x) takes any x and rounds it down to the nearest integer. Find INT(x) for x 4.6, 2.3, and 2. Then find the domain and range. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 48 Name _______________________________________ Date __________________ Class __________________ LESSON 3-2 Practice and Problem Solving C 1. It is a function because each input has exactly one output. 2. It is not a function because 3 is paired with two different outputs. 3. Sample answer Sample explanation I know that a domain value cannot have two different range values, so I changed one domain value to match another domain number. This means one domain member has two range values. 4. The first graph is not a function because a vertical line passes through the curve more than one time. The second graph is a function because a vertical line only passes through the curve once. 5. INT(4.6) 4, INT(2.3), INT(SQRT{2}) 1 Domain and range in general for INT(x) D All real numbers, R All integers Domain and range for INT(x) for given values of x: D {4.6, 2.3, SQRT{2}}, R {3, 1, 4} solution $66 Practice and Problem Solving C 1. D {2, 5, 7, 8}; Sample answer I substituted each value of the range in the function for f(x) and worked backward to solve the equation to find the value of x. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 52