# 3.2 Understanding Relations and Functions-NOTES

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1 Name Class Date. Understanding Relations and Functions-NOTES Essential Question: How do ou represent relations and functions? Eplore A1.1.A decide whether relations represented verball, tabularl, graphicall, and smbolicall define a function; Also A1..A Understanding Relations A relation is a set of ordered pairs (, ) where is the input value and is the output value. The domain is all possible inputs of a relation, and the range is all possible outputs of a relation. For eample, the given relation represents the number of whole-wheat cracker boes sold and the mone earned. { (1, ), (, ), (, 1), (, 16) }. Domain: {1,,, } Range: {,, 1, 16} For the following relation, the input,, is the ages of bos and the output,, is their corresponding height, in inches. {(7, 1), (, 5), (9, 9), (, 5), (, 5), (11, 55), (1, 59)} B Fill the values in the table. Plot the points on the graph Age (r)

2 Complete the mapping diagram. Age (r) State the domain of the relation State the range of the relation Discussion The number appears twice in the column of the table. How man times is it written in the domain? Eplain. Eplain 1 Recognizing Functions A function is a tpe of relation in which there is onl one output value for each input value. For ever input value, there is a unique output value. Eample: =. When =, will alwas be equal to 9. Eample 1 Give the domain and range of each relation. State the corresponding outputs for the given inputs in contet and eplain whether the relation is a function. The given relation represents the number of students and the number of classrooms the school has to have for the corresponding number of students. Students Classrooms 0 5 Domain: {0, 5 } Classrooms 5 The domain represents the number of students. Range: {,, } The range represents the number of classrooms. For an input of 0 students, there is an output of classrooms. For an input of 5 students, there is an output of classrooms. For an input of students, there is an output of classrooms. This relation is a function. Each domain value is paired with eactl one range value Students Students Classrooms 0 5

3 B The given relation represents the amount of gas in gallons and the distance traveled in miles from that amount of gas Domain: The domain represents Range: The range represents. This relation range value. a function. Each domain value is paired with. If each month in a ear was paired with all the possible numbers of das in the month, will the result be a function? Eplain.

4 Your Turn Give the domain and range of each relation and interpret them in contet. State the corresponding outputs for the given inputs in contet and eplain whether the relation is a function.. The relation represents the number of books sold and the price for the corresponding number of books. Number of books sold Price (\$) Books Sold Price (\$) Price (\$) Books Sold. The relation represents the time spent eercising and the number of calories burned during that time. Calories burned Calories Burned Calories burned 5 0

5 Eplain Understanding the Vertical Line Test A test, called the vertical line test, can be used to determine if a relation is a function. The vertical line test states that a relation is a function if and onl if a vertical line does not pass through more than one point on the graph of the relation. Eample Use the vertical line test to determine if each relation is a function. Eplain. Draw a vertical line through each point of the graph. Does an vertical line touch more than one point? Yes Since a vertical line does pass through more than one point, the graph fails the vertical line test. So, the relation is not a function Age B Draw a vertical line through each point of the graph. 0 Does an vertical line touch more than one point? Since a vertical line one point, the graph the relation a function. pass through more than the vertical line test. So, Wh does the vertical line test work? Your Turn Use the vertical line test to determine if each relation is a function

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? LESSN. Solving Sstems of Linear Equations b Graphing ESSENTIAL QUESTIN How can ou solve a sstem of equations b graphing? Epressions, equations, and relationships.9 Identif and verif the values of and