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5 (blue) that was above the x-axis is still above the \ x-axis for y = |x - 5| (green).\ \>", "Item", CellChangeTimes->{{3.459618060781809*^9, 3.4596180781869445`*^9}, { 3.4596181333396645`*^9, 3.459618163712721*^9}}], Cell["\<\ Every part of y = x - 5 (blue) that was above the x-axis is still above the \ x-axis for y = |x - 5| (green).\ \>", "Item", CellChangeTimes->{{3.459618060781809*^9, 3.4596180781869445`*^9}, { 3.4596181333396645`*^9, 3.459618163712721*^9}}] }, Open ]], Cell["\<\ What is the difference in the blue function and the green function? \ \>", "Text", CellChangeTimes->{{3.4585131609066315`*^9, 3.458513175672162*^9}, { 3.458515829248929*^9, 3.458515862045594*^9}, {3.4595024504009457`*^9, 3.4595024617603207`*^9}, {3.460302218557844*^9, 3.4603022191984615`*^9}}], Cell["\<\ g (x) = 2 f (x). (The red function values are all twice the \ corresponding blue function' s values.)\ \>", "Answer", CellChangeTimes->{ 3.4595323664349117`*^9, {3.4595324045130367`*^9, 3.4595324185599117`*^9}, { 3.459602706419465*^9, 3.4596027092164116`*^9}, {3.4596027432329073`*^9, 3.4596027455142155`*^9}, {3.459605862748063*^9, 3.4596058687788877`*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 1", "Subsubsection", CellChangeTimes->{{3.4463006149870167`*^9, 3.4463006181425595`*^9}}], Cell["\<\ For the following descriptions, plot the graphs that are described on the \ same set of axes.\ \>", "Text", CellChangeTimes->{{3.4595026155109243`*^9, 3.4595026541832943`*^9}, { 3.4603022639478884`*^9, 3.4603023036192555`*^9}, {3.460302471851477*^9, 3.4603024797420015`*^9}}], Cell[TextData[{ "1) y = ", Cell[BoxData[ FormBox[ SuperscriptBox["x", "2"], TraditionalForm]], FormatType->"TraditionalForm"], " - 8, " }], "Text", CellChangeTimes->{{3.460302316619089*^9, 3.460302391883751*^9}}], Cell["(a) The parabola as is in blue.", "Text", CellChangeTimes->{{3.460302396508692*^9, 3.460302404211718*^9}}], Cell["(b) The absolute value of the parabola in orange.", "Text", CellChangeTimes->{{3.460302405992945*^9, 3.460302425492696*^9}}], Cell["\<\ (c) Graph (b) shifted up 2 and left 4 in green.\ \>", "Text", CellChangeTimes->{{3.460302427633293*^9, 3.460302455398563*^9}, { 3.460302571100207*^9, 3.4603025763970137`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.4603024820700965`*^9, 3.4603026293182116`*^9}, 3.4603051809611464`*^9}], Cell["\<\ \ \>", "Text", CellChangeTimes->{3.460305186476418*^9}], Cell["\<\ 2) What do you notice about the location of the sharp points of the orange \ graph?\ \>", "Text", CellChangeTimes->{{3.460302641036812*^9, 3.460302653974146*^9}}], Cell["", "Answer"], Cell["\<\ \ \>", "Text", CellChangeTimes->{3.4603052376304116`*^9}], Cell["\<\ 3) Plot the graph of g(x) = |f(x)| such that f(x) is a parabola with no \ horizontal or vertical stretch and such that g(x) has sharp points at (-6,0) \ and (2,0).\ \>", "Text", CellChangeTimes->{{3.460302663114654*^9, 3.4603027917380075`*^9}}], Cell[TextData[StyleBox["Hint: Use your answer to #2 above to find the \ function f(x).", FontSlant->"Italic"]], "Text", CellChangeTimes->{{3.460302798112926*^9, 3.460302820112644*^9}}], Cell[BoxData[ RowBox[{"Expand", "[", RowBox[{ RowBox[{"(", RowBox[{"x", "-", RowBox[{"(", RowBox[{"-", "6"}], ")"}]}], ")"}], "*", RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}]}], "]"}]], "Input", CellChangeTimes->{{3.460302834674958*^9, 3.4603028801743755`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.460302884689943*^9, 3.46030294857975*^9}, 3.4603052528018007`*^9}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Concept Exploration", "Subsection", CellChangeTimes->{{3.4462996971190157`*^9, 3.446299723414039*^9}, { 3.456614564946227*^9, 3.4566145737392273`*^9}}], Cell[CellGroupData[{ Cell["Absolute Value inside the function.", "Subsubsection", CellFrameColor->RGBColor[ 0.6449835965514611, 0.758632791638056, 0.2516823071641108], CellChangeTimes->{{3.4572682917399263`*^9, 3.457268298197912*^9}, { 3.45726861307681*^9, 3.4572686272230935`*^9}, {3.458515362189418*^9, 3.458515368751876*^9}, {3.459502205277475*^9, 3.459502211043063*^9}, { 3.4595031990942054`*^9, 3.4595032048442054`*^9}, {3.4603031436085033`*^9, 3.4603031504834156`*^9}}, FontColor->RGBColor[ 0.6449835965514611, 0.758632791638056, 0.2516823071641108]], Cell["\<\ What happens if we take the absolute value of just a portion of a graph, \ instead of the entire graph? 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(i.e., will the same orange \ graph result if the absolute value operator is placed around any term or \ terms?) Let's investigate. (next slide).\ \>", "Text", CellChangeTimes->{{3.460303736710287*^9, 3.460303789443987*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 2", "Subsubsection", CellChangeTimes->{{3.4463006149870167`*^9, 3.4463006181425595`*^9}, { 3.4595046093011703`*^9, 3.4595046096917953`*^9}}], Cell["\<\ Graph the following functions and their reciprocals. 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Click on the plus sign \ beside the slider to open the animation controls. 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Typeset`skipInitDone$$}, "Body" :> Plot[$CellContext`x^2 - $CellContext`h$$ Abs[$CellContext`x] - 12, {$CellContext`x, -10, 10}, AspectRatio -> Automatic, PlotRange -> {-20, 3}, PlotStyle -> {Thick, Green}], "Specifications" :> {{$CellContext`h$$, -5, 5}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{403., {242.40625, 248.59375}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.460304857244379*^9, 3.460304867525629*^9}}] }, Open ]], Cell["\<\ 2) What happens to the graph as h goes from negative to positive?\ \>", "Text", CellChangeTimes->{{3.4595053149730453`*^9, 3.4595053471136703`*^9}, { 3.460304841588129*^9, 3.460304841744379*^9}, {3.460304893572504*^9, 3.460304908291098*^9}}], Cell["", "Answer", 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"Subsubsection", CellChangeTimes->{{3.457269248476753*^9, 3.457269257724622*^9}}], Cell["1) What happens as h increases?", "Text", CellChangeTimes->{{3.4595052265355453`*^9, 3.4595052560667953`*^9}, { 3.460304785260004*^9, 3.460304790478754*^9}}], Cell["\<\ As h increases, the vertex moved farther away from the y-axis and became more \ negative.\ \>", "Answer", CellChangeTimes->{{3.4595052697855453`*^9, 3.4595052715824203`*^9}, 3.459607026430394*^9, {3.460305573792399*^9, 3.460305610916686*^9}}], Cell["\<\ 2) What happens to the graph as h goes from negative to positive?\ \>", "Text", CellChangeTimes->{{3.4595053149730453`*^9, 3.4595053471136703`*^9}, { 3.460304841588129*^9, 3.460304841744379*^9}, {3.460304893572504*^9, 3.460304908291098*^9}}], Cell["\<\ The second \"hump\" disappeared and the smooth vertex of the parabola is \ \"replaced\" with a sharp point on the y-axis.\ \>", "Answer", CellChangeTimes->{{3.4595053488480453`*^9, 3.4595053506605453`*^9}, 3.4596070287114105`*^9, {3.4603056636500487`*^9, 3.4603057007118373`*^9}}], Cell["\<\ 3) What does this imply about the \"original function,\" or the parabola \ without the absolute value function inside?\ \>", "Text", CellChangeTimes->{{3.4595053149730453`*^9, 3.4595053471136703`*^9}, { 3.460304841588129*^9, 3.460304841744379*^9}, {3.460304893572504*^9, 3.460304959287834*^9}}], Cell["\<\ In general, the coefficient of the linear term has a lot to do with where, \ vertically, the vertex of the parabola lies.\ \>", "Answer", CellChangeTimes->{{3.4595053488480453`*^9, 3.4595053506605453`*^9}, 3.4596070287114105`*^9, {3.4603075251412673`*^9, 3.4603075484537673`*^9}}], Cell[TextData[{ "4) To check and see if your answer to number 3 is correct, copy the \ demonstration from number 2, and using ", StyleBox["Mathematica", FontSlant->"Italic"], "'s list notation { }, graph a static absolute value graph and a parabola \ with the parameter h that changes." }], "Text", CellChangeTimes->{{3.460304968427874*^9, 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RGBColor[0.145098, 0.545098, 0.858824]], Cell[ StyleData["Subtitle"], CellMargins -> {{24, Inherited}, {12, 12}}, MenuPosition -> 1100, MenuCommandKey -> "2", FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.301961, 0.631373, 0.890196]], Cell[ CellGroupData[{ Cell[ StyleData["Section"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{24, Inherited}, {6, 24}}, MenuPosition -> 1300, MenuCommandKey -> "4", FontFamily -> "Helvetica", FontSize -> 18, FontWeight -> "Bold", FontColor -> RGBColor[0.87451, 0.411765, 0.0745098], Background -> RGBColor[0.992157, 0.984314, 0.941176]], Cell[ StyleData["Section", "SlideShow"], FontSize -> 26], Cell[ StyleData["Section", "Printout"], CellMargins -> {{36, Inherited}, {Inherited, 18}}, FontSize -> 12], Cell[ StyleData["Section", "ColorPrintout"], CellMargins -> {{36, Inherited}, {Inherited, 18}}, FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsection"], CellDingbat -> None, CellMargins -> {{24, Inherited}, {Inherited, 18}}, MenuPosition -> 1310, MenuCommandKey -> "5"], Cell[ StyleData["Subsection", "SlideShow"], CellMargins -> {{28, Inherited}, {Inherited, 18}}, MenuPosition -> 1310, MenuCommandKey -> "5", FontSize -> 22]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubsection"], CellDingbat -> Cell["\[EmptySmallSquare]"], CellMargins -> {{50, Inherited}, {2, 18}}, MenuPosition -> 1320, MenuCommandKey -> "6", FontFamily -> "Helvetica", FontSize -> 13, FontWeight -> "Bold", FontColor -> RGBColor[0.909804, 0.596078, 0.25098]], Cell[ StyleData["Subsubsection", "Presentation"], CellMargins -> {{80, Inherited}, {3, 15}}, FontSize -> 24], Cell[ StyleData["Subsubsection", "Printout"], CellMargins -> {{36, Inherited}, {Inherited, 12}}, FontSize -> 10], Cell[ StyleData["Subsubsection", "ColorPrintout"], CellMargins -> {{36, Inherited}, {Inherited, 12}}, FontSize -> 10]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Heading cells", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["LabelStyle"], CellSize -> {136, Inherited}, CellBaseline -> Baseline, TextAlignment -> Right, FontFamily -> "Helvetica", FontWeight -> "Bold"], Cell[ StyleData["LabelStyle", "SlideShow"], CellSize -> {148, Inherited}, FontSize -> 16]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["LabelStyleShort"], CellSize -> {64, Inherited}, CellBaseline -> Baseline, TextAlignment -> Right, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold"], Cell[ StyleData["LabelStyleShort", "SlideShow"], CellSize -> {72, Inherited}, CellBaseline -> Baseline, TextAlignment -> Right, FontFamily -> "Helvetica", FontWeight -> "Bold"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TeacherName"], CellMargins -> {{24, Inherited}, {6, 24}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Teacher: "], "LabelStyleShort"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1200, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["TeacherName", "SlideShow"], FontSize -> 16]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ClassName"], CellMargins -> {{24, Inherited}, {6, 0}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Class: "], "LabelStyleShort"], None}, { None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1210, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["ClassName", "SlideShow"], FontSize -> 16]}, Closed]], Cell[ StyleData["Course"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Course: "], "LabelStyle"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1400, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["ActivityLength"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Activity Length: "], "LabelStyle"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1410, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["NCTMStandard"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["NCTM Standard: "], "LabelStyle"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1420, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["Prerequisites"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Prerequisites: "], "LabelStyle"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1430, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["Objectives"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Objectives: "], "LabelStyle"], None}, {None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1440, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["ActivityType"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Type of Activity: "], "LabelStyle"], None}, { None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1450, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["ReferenceMaterial"], CellMargins -> {{24, Inherited}, {0, 7}}, CellFrameMargins -> 0, CellFrameLabels -> {{ Cell[ TextData["Reference Material: "], "LabelStyle"], None}, { None, None}}, CellFrameLabelMargins -> 0, MenuPosition -> 1450, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Plain", FontSlant -> "Plain"]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[ CellGroupData[{ Cell["Display", "Subsection"], Cell[ CellGroupData[{ Cell[ StyleData["Text"], CellMargins -> {{28, Inherited}, {Inherited, Inherited}}, CounterIncrements -> "Text", MenuPosition -> 1600, MenuCommandKey -> "7", FontFamily -> "Helvetica", FontColor -> RGBColor[0.196078, 0.196078, 0.196078]], Cell[ StyleData["Text", "SlideShow"], CellMargins -> {{28, Inherited}, {8, 8}}, FontSize -> 16]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["MathCaption"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{68, 12}, {0, 20}}, PageBreakBelow -> False, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.819455, 0.804242, 0.663142], CellFrameLabelMargins -> 4, LineSpacing -> {1, 4}, ParagraphSpacing -> {0, 8}, MenuPosition -> 1600, MenuCommandKey -> "8", FontFamily -> "Helvetica", FontSize -> 12], Cell[ StyleData["MathCaption", "Presentation"], FontSize -> 24], Cell[ StyleData["MathCaption", "SlideShow"], CellMargins -> {{72, 36}, {0, 36}}, FontSize -> 16], Cell[ StyleData["MathCaption", "Printout"], CellMargins -> {{54, 0}, {0, 14}}, Hyphenation -> True, FontFamily -> "Times", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Example"], CellDingbat -> Cell[ TextData["Example: "], FontWeight -> "Bold"], CellMargins -> {{94, Inherited}, {18, 18}}, MenuPosition -> 1600, FontFamily -> "Helvetica", FontColor -> RGBColor[0.196078, 0.196078, 0.196078]], Cell[ StyleData["Example", "SlideShow"], FontSize -> 16]}, Closed]], Cell[ StyleData["Answer"], CellFrame -> 1., CellMargins -> {{18, Inherited}, {Inherited, 6}}, CellFrameMargins -> 10, CellFrameLabels -> {{ Cell[ TextData["Answer:"], "LabelStyleShort"], None}, {None, None}}, MenuPosition -> 1600, FontFamily -> "Helvetica", FontSize -> 16, FontColor -> RGBColor[0.196078, 0.196078, 0.196078], Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell["Lists", "Subsection"], Cell[ CellGroupData[{ Cell["Bulleted", "Subsubsubsection"], Cell[ CellGroupData[{ Cell[ StyleData["Item"], CellMargins -> {{78, 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