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Functions reading passage
- 1. Functions Accordingto Corestandards.org,afunctionis“arule that assignseachinputexactlyone output.”The definitioncontinueswith“the graphof a functionisa setof orderedpairsconsistingof an inputandthe correspondingoutput.” In orderto betterunderstandfunctions,let’stake acloserlookatthe definition givenabove. First,let’sexaminethe wordsinputandoutput.Inmath,inputandoutputgenerallyreferto x and y valuesof a givenequation.Forexample,inthe equation y=2x + 1, we can inputa numberinfor x.After solving,we getan output,whichisthe value fory. If we lookback at the original definition,itsays“each inputhas exactlyone output.”Inotherwords,there can’tbe any repeatsinthe input(x).Let’slookat some setsof data and explainwhytheyare functions: (-3,0) (2,5) (4,5) (-5,0) Thisis a function because there are norepeatvaluesof x (4, 5) (3, -7) (4,9) (6, 8) Thisis NOTa function,because 4isrepeatedasa value of x ThisIS a functionbecause there are norepeatvaluesof x ThisIS a functionbecause novalues Thisis NOTa functionbecause some of of x wouldrepeat. the x valuesrepeat. As youmay have noticedfromthe examplesabove,functionscanbe representedasequations, tablesor graphs. Input Output 4 1 5 3 6 1
- 2. Is it a Function? What is the easiest way to determind a set or ordered pairs, a table or a graph is a function? We will discuss a couple different options to determine a function. Functions as Ordered Pairs When given a set of ordered pairs, there are two methods: Method #1: Look for a repeat in the x (1, 3), (2, 5), (4, 6), (4, 10) Method #2: Graph it and use the vertical line test (we will discuss this later) Method #3: Map it Functions as a Table When given in a table, there are two methods: Method #1: Look for a repeat in the input/x Method #2: Graph it and use the vertical line test Functions as a Graph When given a graph, there is one method: Method #1: Vertical Line Test If you drawa vertical lineand ittouches the graph in more than one place, it’s not a function. Therefor, if you draw a vertical line and it touches the graph in only one place, it is a function. Since 4 repeats in the x, it is NOTa function. Input Output 3 6 4 8 5 10 6 12 Since there are no repeats in the input, this IS a function. The input 2 has more than one output, NOTa function.