Function and Non-Function Equations
?W2KLesson QuestionWords to KnowFill in this table as you work through the lesson. You may also use the glossary to help you.Identifyfunctions.functions fromscenarios.areDetermine ifDetermine if relationsarefrom tables, graphs, and equations.Lesson Goalsfunctiona relation in which each element of the input is mapped to(paired with) exactlyelement of the outputinputa value that is transformed by a process and becomesoutputthe result of anthat has been transformed by a processW2KWords to KnowInput / Output TableFill in the missing values in the table.Inputy = 4(?2) + 5(x, y)y = ?8 + 5y =(0,)y = 4(1) + 5y =+ 5y = 9ordered pairy = 4x + 5relationa set ofpairsvertical line testa test showing that if any vertical line passes through no more than one point of the graph of a relation, then the relation isaxy?2?3?11051213Identifying Functionsy = x2 ? 3The input 9 is paired with functiontwo different outputs.y2 = xa functionA function is a relation in which one input is paired with exactlyoutput.Slide634091223543835521253236034355182721639860Tables of EquationsEquations are functions or not functions.y2 = x + 12x2 + y2 = 9y = 3x + 4not a functiona functionxy?3?3?334?444xy?300?30330xy?4?8?111741624xy?36?1?236522xy9?31?193255SlideFunction and Non-Function EquationsEXAMPLE4Functionsy = 41y = 2 x + 31 = y ? 5x y = x2 + 4y = x2 + 3x ?12They all have= somewherein the equation. So that’s what makes these all functions. y is going to equalnumber.Not Functionsx = ?6y2 = x + 4y2 + x2 = 25It’s not a function if you have= some number, or if you have in the equation.The Vertical Line TestConsider the points in the following table:Plot the points from the table on thecoordinate plane and draw the line through them.Vertical line test: If any vertical line passes through no more thanpoint, then the relation isa.SlideFunctions Versus Non-Functions??a FunctionyxxEach line passes through exactlypoint on the graph.The vertical lines go throughthan one point.yyxyx8xy?3?4?1014y42x?4?224?2?4SlideDetermine Whether a Real-World Relationship is a FunctionREAL-WORLD CONNECTIONDetermine if the following scenario represents a function.Is the height of a football kicked across a field a function of the time? Theis a function of the.12y6050Height (feet)40302010x123456Time (seconds)12SlideDetermining Whether a Real-World Relationship is a FunctionEXAMPLEA survey asked high school math students their ages and heights. The results are shown in the table. Is the height a function of the age?Age (yrs)Height (in.)156016621667176518631964This scenario isa function.Height (in.)Circle the points that represent an input with more than one output.68y66646260x1516171819Age (yrs)?What is a function and how can I identify one?Lesson QuestionAnswerSummaryIntroduction to FunctionsUse this space to write any questions or thoughts about this lesson. ................
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