U1L1 Exploring Relations PDF

Unit 1, Lesson 1: Exploring Relations Learning Target □ I can recognize relations represented in different forms. Collaborative Activity: Representing Mathematical Rules and Relations An input-output rule is a rule that takes an input value and uses...

Unit 1, Lesson 1: Exploring Relations Learning Target □ I can recognize relations represented in different forms. Collaborative Activity: Representing Mathematical Rules and Relations An input-output rule is a rule that takes an input value and uses it to determine an output value. Input Rule Output For example, in the table shown, a rule was used to get each output value from its corresponding input value. Input −5 −1 0 2.5 6 3 Output −15 −1 0 7.5 18 1. Work with your partner to determine the rule for the previous table. Then, complete the statement to describe the rule. input input Each value is the result of taking the output output adding 10 to it. and dividing it by 3. multiplying it by 3. subtracting 10 from it. © Accelerate Learning Inc. - All Rights Reserved Unit 1 | 3 2. Work with your partner to complete the input-output table for each rule. The first row has been completed as an example. Rule Table of Values Input Output 3 4 7 Add 1, and then 2.35 Input Output multiply by 4. 42 −1 𝒙 𝒚 −12 Write 1 if the input is −5 x odd; write 0 if the y input is even. 6 19 Each of the tables represent a relation. A relation is a set of input-output pairs. 4 | Unit 1 © Accelerate Learning Inc. - All Rights Reserved Relations can also be represented by mapping diagrams. The Input Output mapping diagram shown represents input-output pairs for the rule “divide by 4, and then add 2.” –8 4 1 0 8 2 14 3. Work with your partner to complete the statements. In a mapping diagram, an input is mapped to its corresponding input output output using an arrow. In the mapping diagram above, the input 8 results in 4 an output of 0 for the relation shown. 21 4 4. Work with your partner to complete the mapping diagram for each rule. Rule Mapping Diagram Input Output –4 Find the square 0 –2 Input Output root(s) of the input. 4 0 16 2 4 x y Subtract 3, and then –2 x y multiply by 12. 0 5 © Accelerate Learning Inc. - All Rights Reserved Unit 1 | 5 5. Complete the statements. input values inputs. The of a relation depend on the values used for the outputs. output values Therefore, the inputs are the dependent variables, and the outputs are independent variables, the dependent variables. independent variables. Relations can be represented using graphs. Each relation in the table below is shown alongside its mapping diagram and graph. Relation Mapping Diagram Graph y 5 4 x y 3 2 –2 1 –1 x Relation A 0 –3 -5 -4 -3 -2 -1 0 1 2 3 4 5 1.5 5 -1 2 3 -2 -3 -4 -5 y 5 x y 4 3 2 1 1 Relation B –4 x 4 5 -4 -3 -2 -1 0 1 2 3 4 5 –1 -1 -2 -3 -4 6 | Unit 1 © Accelerate Learning Inc. - All Rights Reserved 6. With your partner, discuss your observations in comparing the mapping diagrams and graphs for each relation. 7. Complete the statements. 2 The mapping diagram for each of the relations has 3 input-output pairs 4 2 indicated by arrows. The graph showing the same relation has 3 points. 4 𝑥-value The input value from the mapping diagram matches the of each 𝑦-value point on the graph, and its corresponding output value from the mapping diagram 𝑥-value matches the of each point on the graph. 𝑦-value A relation can also be represented by a set of ordered pairs. 8. The set of ordered pairs shown can be used to represent relation A from the previous table. {(−2, − 3), 0, 5 , (1.5, − 1), (3, − 3)} 2 Write the set of ordered pairs that represents relation B from the previous table. © Accelerate Learning Inc. - All Rights Reserved Unit 1 | 7  Guided Activity: Representing Relations A relation is any set of input-output pairs, which can be represented using a table of values, a mapping diagram, a set of ordered pairs, or a graph. 1. Complete the statements. dependent In a relation, the set of input values is the independent variable. The input 𝑥-value value is the in an ordered pair. The set of output values of a relation is 𝑦-value dependent 𝑥-value the independent variable. The output value is the in an ordered 𝑦-value pair. The relation can be represented as a set of ordered pairs or on a graph. Wrap-Up: Reflection 1. Plot a point in one of the quadrants to indicate Interesting your level of interest in today’s learning targets and your understanding of them. 2. Write one question you have about relations after today’s lesson. Confusing Makes sense Uninteresting 8 | Unit 1 © Accelerate Learning Inc. - All Rights Reserved