Function Input and OutputThe Magic BoxSlide 3Output ValuesEvaluating a FunctionSlide 6Finding Input ValuesSlide 8Slide 9Possible Solution StrategiesFor You to TryFunction Input and OutputFunction Input and OutputLesson 2.1Lesson 2.122The Magic BoxThe Magic BoxConsider a box that Consider a box that receives numbers in receives numbers in the topthe topAnd alters them And alters them somehow and sends somehow and sends a (usually) different a (usually) different number out the spoutnumber out the spoutFor each of the number combinations, can you figure out the "rule" which alters the number?1-34331Today we look at the mathematical way of talking about the "rule"Today we look at the mathematical way of talking about the "rule"33The Magic BoxThe Magic BoxConsider a box that Consider a box that receives numbers in receives numbers in the topthe topAnd alters them And alters them somehow and sends somehow and sends a (usually) different a (usually) different number out the spoutnumber out the spout44Output ValuesOutput ValuesOutput Value Output Value Evaluating the FunctionEvaluating the FunctionSubstitute the input value for Substitute the input value for every instance of the independentevery instance of the independentvariable in the functionvariable in the functionInput ValueOutput value25( )1xh xx-=-f(x)55Evaluating a FunctionEvaluating a FunctionGivenGivenDetermine the value of the function h Determine the value of the function h when x = 2 h(2) = ?when x = 2 h(2) = ?Determine h(-4)Determine h(-4)25( )1xh xx-=-22 5 3(2) 12 1 3h- -= = =--24 5 9( 4)( 4) 1 15h- - -- = =- -66Evaluating a FunctionEvaluating a FunctionCalculator can evaluate functionsCalculator can evaluate functionsAlso possible to evaluate for symbolic Also possible to evaluate for symbolic values of the independent variablevalues of the independent variable77Finding Finding InputInput Values ValuesConsider the function Consider the function as a box with a funnelas a box with a funneland spout …and spout …What if we knew what was comingWhat if we knew what was comingoutout and wished to know what went and wished to know what went inin that that gave that resultgave that resultIndependent VariableDependent variable( ) 3??h xx=-=25( )1xh xx-=-h(x)88Finding Input ValuesFinding Input ValuesTry using the “solve ( )” command on your Try using the “solve ( )” command on your calculatorcalculatorPress Diamond, Enter to force decimal answer99Finding Input ValuesFinding Input ValuesGiven g(x) = xGiven g(x) = x22 – 2x + 4 – 2x + 4g(x) = 12 x = ?g(x) = 12 x = ?Create an equation using the formula and Create an equation using the formula and the outputthe output 12 = x12 = x22 – 2x + 4 – 2x + 4Solve for all possible values of x which Solve for all possible values of x which make that statement truemake that statement true20 2 80 ( 4) ( 2)4 2x xx xx or x= - -= - � += =-1010Possible Solution StrategiesPossible Solution StrategiesAlgebraicAlgebraic–factor the quadraticsfactor the quadraticsLook at tables of valuesLook at tables of valuesGraph the functionGraph the function–create a horizontal line (i.e. at y = 4.4)create a horizontal line (i.e. at y = 4.4)–note the intersectionnote the intersectionUse the solve command on the calculatorUse the solve command on the calculator1111For You to TryFor You to TryTry together in class on page 64Try together in class on page 64–Ex 8, 9Ex 8, 9AssignmentAssignment–Page 66Page 66–Exercises 3, 5, 10, 13, 15, 19, 25, Exercises 3, 5, 10, 13, 15, 19, 25, 29, 31, 35, 3729, 31, 35,