(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     17234,        497]
NotebookOptionsPosition[     16478,        468]
NotebookOutlinePosition[     16837,        484]
CellTagsIndexPosition[     16794,        481]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Domain and Range", "Title",
 CellChangeTimes->{{3.5666066674381123`*^9, 3.56660667007513*^9}},
 TextAlignment->Center],

Cell["\<\
by Ruth Dover
Illinois Mathematics and Science Academy\
\>", "Subsubtitle",
 CellChangeTimes->{{3.6925544130802107`*^9, 3.692554426152443*^9}}],

Cell[TextData[{
 "Edit the first two lines below in each example to enter \.08your own \
function and values for ",
 StyleBox["xmin",
  FontSlant->"Italic"],
 " and ",
 StyleBox["xmax",
  FontSlant->"Italic"],
 ".  Execute the cell by pressing Shift-Enter. The range is shown in ",
 StyleBox["magenta",
  FontColor->RGBColor[1, 0, 1]],
 " along the ",
 StyleBox["y",
  FontSlant->"Italic"],
 "-axis. \nSeveral examples are shown to allow you to see different types of \
functions (and to make editing easier).\n",
 StyleBox["Important Note:",
  FontColor->RGBColor[1, 0, 0]],
 "  You\[CloseCurlyQuote]ll have to figure out the endpoints for yourself!\n\
",
 StyleBox["Another Important Note:",
  FontColor->RGBColor[1, 0, 0]],
 "  There are some functions where this just doesn\[CloseCurlyQuote]t work \
well!  (Sorry!)"
}], "Text",
 CellChangeTimes->{{3.566738606114092*^9, 3.566738726405675*^9}, {
  3.5667388721612377`*^9, 3.5667388726013002`*^9}, {3.566738921734202*^9, 
  3.566738957919281*^9}, {3.5667390472223587`*^9, 3.566739049075735*^9}, {
  3.566739199930016*^9, 3.566739228423428*^9}, {3.692554289574316*^9, 
  3.692554312432042*^9}, {3.692554775425734*^9, 3.692554783468959*^9}, {
  3.692554817142475*^9, 3.692554829247233*^9}}],

Cell[TextData[StyleBox["Example 1",
 FontColor->RGBColor[1, 0, 0]]], "Text",
 CellChangeTimes->{{3.5667387831488667`*^9, 3.566738785187373*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "2"], "-", 
    RowBox[{"2", "x"}], "+", "3"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xmin", "=", 
   RowBox[{"-", "1"}]}], ";", 
  RowBox[{"xmax", "=", "4"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"stepsize", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"xmax", "-", "xmin"}], ")"}], "/", "1000."}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypl", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"x", ",", "xmin", ",", " ", "xmax"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypts", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Magenta", ",", 
       RowBox[{"PointSize", "[", "Large", "]"}], ",", " ", 
       RowBox[{"If", "[", 
        RowBox[{
         RowBox[{"NumberQ", "[", 
          RowBox[{"f", "[", "k", "]"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"0", ",", 
            RowBox[{"f", "[", "k", "]"}]}], "}"}], "]"}]}], "]"}]}], "}"}], 
     ",", " ", 
     RowBox[{"{", 
      RowBox[{"k", ",", " ", "xmin", ",", "xmax", ",", " ", "stepsize"}], 
      "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"mypl", ",", " ", 
   RowBox[{"Graphics", "[", "mypts", "]"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.5667390679067783`*^9, 3.5667390745045233`*^9}, {
  3.56673912871327*^9, 3.56673918547882*^9}, {3.56673924753957*^9, 
  3.566739248586151*^9}, {3.566739363123518*^9, 3.566739436273593*^9}, {
  3.6925547228543043`*^9, 3.69255472374049*^9}, {3.692554795036317*^9, 
  3.692554798815055*^9}}],

Cell[TextData[StyleBox["Example 2",
 FontColor->RGBColor[1, 0, 0]]], "Text",
 CellChangeTimes->{{3.566738787893441*^9, 3.566738794622238*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], ":=", 
   RowBox[{"Floor", "[", "x", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xmin", "=", 
   RowBox[{"-", "1"}]}], ";", 
  RowBox[{"xmax", "=", "4"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"stepsize", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"xmax", "-", "xmin"}], ")"}], "/", "1000."}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypl", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"x", ",", "xmin", ",", " ", "xmax"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypts", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Magenta", ",", 
       RowBox[{"PointSize", "[", "Large", "]"}], ",", " ", 
       RowBox[{"If", "[", 
        RowBox[{
         RowBox[{"NumberQ", "[", 
          RowBox[{"f", "[", "k", "]"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"0", ",", 
            RowBox[{"f", "[", "k", "]"}]}], "}"}], "]"}]}], "]"}]}], "}"}], 
     ",", " ", 
     RowBox[{"{", 
      RowBox[{"k", ",", " ", "xmin", ",", "xmax", ",", " ", "stepsize"}], 
      "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"mypl", ",", " ", 
   RowBox[{"Graphics", "[", "mypts", "]"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.566739253779066*^9, 3.566739254817965*^9}, {
  3.692554856339755*^9, 3.692554857722674*^9}}],

Cell[TextData[{
 StyleBox["Example 3",
  FontColor->RGBColor[1, 0, 0]],
 ": Piecewise functions, including disconnected domains"
}], "Text",
 CellChangeTimes->{{3.56673879869228*^9, 3.56673880081092*^9}, {
  3.56673888867267*^9, 3.566738912054328*^9}, {3.5667390045014668`*^9, 
  3.5667390049093018`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], ":=", 
   TagBox[GridBox[{
      {"\[Piecewise]", GridBox[{
         {
          RowBox[{"x", "-", "1"}], 
          RowBox[{"x", "\[LessEqual]", "0"}]},
         {"x", 
          RowBox[{"x", ">", "2"}]},
         {"Undefined", "True"}
        },
        AllowedDimensions->{2, Automatic},
        Editable->True,
        GridBoxAlignment->{
         "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxItemSize->{
         "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
           "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.84]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}},
        Selectable->True]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
       "RowsIndexed" -> {}},
     GridBoxItemSize->{
      "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.35]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    "Piecewise",
    DeleteWithContents->True,
    Editable->False,
    SelectWithContents->True,
    Selectable->False]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xmin", "=", 
   RowBox[{"-", "1"}]}], ";", 
  RowBox[{"xmax", "=", "4"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"stepsize", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"xmax", "-", "xmin"}], ")"}], "/", "1000."}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypl", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"x", ",", "xmin", ",", " ", "xmax"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mypts", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Magenta", ",", 
       RowBox[{"PointSize", "[", "Large", "]"}], ",", " ", 
       RowBox[{"If", "[", 
        RowBox[{
         RowBox[{"NumberQ", "[", 
          RowBox[{"f", "[", "k", "]"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"0", ",", 
            RowBox[{"f", "[", "k", "]"}]}], "}"}], "]"}]}], "]"}]}], "}"}], 
     ",", " ", 
     RowBox[{"{", 
      RowBox[{"k", ",", " ", "xmin", ",", "xmax", ",", " ", "stepsize"}], 
      "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"mypl", ",", " ", 
   RowBox[{"Graphics", "[", "mypts", "]"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.566739259683053*^9, 3.5667392607464733`*^9}, {
  3.6925548708531427`*^9, 3.692554872472105*^9}}],

Cell[CellGroupData[{

Cell["Version 2: For connected domains and ranges only", "Subtitle",
 CellChangeTimes->{{3.566734121302785*^9, 3.566734141037298*^9}, 
   3.5667385880040903`*^9, {3.5667390210681*^9, 3.566739022228278*^9}}],

Cell[TextData[{
 "Edit the first two lines below to enter \.08your own function and values \
for ",
 StyleBox["xmin",
  FontSlant->"Italic"],
 " and ",
 StyleBox["xmax",
  FontSlant->"Italic"],
 ". The domain is shown in ",
 StyleBox["purple",
  FontColor->RGBColor[0.5, 0, 0.5]],
 " and the range is shown in ",
 StyleBox["magenta",
  FontColor->RGBColor[1, 0, 1]],
 " along the respective axes.\nExecute the cell by pressing Shift-Enter.  \
Then use the sliders to view the domain and range over subintervals of the \
entire graph."
}], "Text",
 CellChangeTimes->{{3.566606677568398*^9, 3.566606712271985*^9}, {
  3.566606754094748*^9, 3.5666068116842737`*^9}, {3.566607041277651*^9, 
  3.5666070812896357`*^9}, {3.566649195173007*^9, 3.5666491962436037`*^9}, {
  3.566650959193967*^9, 3.566651014613235*^9}, {3.5666511667997503`*^9, 
  3.566651174524809*^9}, {3.566651224910095*^9, 3.566651237883163*^9}, {
  3.566732978498595*^9, 3.566732982184987*^9}, {3.5667341457730083`*^9, 
  3.566734146188847*^9}, {3.692554967404297*^9, 3.692555022204525*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "3"], "-", 
    RowBox[{"3", "x"}], "+", "1"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"xmin", "=", 
    RowBox[{"-", "2"}]}], ";", 
   RowBox[{"xmax", "=", "2.5"}], ";"}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
   "Leave", " ", "the", " ", "rest", " ", "of", " ", "the", " ", "coding", 
    " ", 
    RowBox[{"alone", "!"}]}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"xmax", "-", "xmin"}], ")"}], "/", "25"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"x", ",", " ", 
       RowBox[{"Min", "[", 
        RowBox[{
         RowBox[{"-", "0.1"}], ",", 
         RowBox[{"xmin", "-", "a"}]}], "]"}], ",", " ", 
       RowBox[{"Max", "[", 
        RowBox[{"0.1", ",", 
         RowBox[{"xmax", "+", "a"}]}], "]"}]}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", 
     RowBox[{"AxesOrigin", " ", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}], ",", 
     RowBox[{"Epilog", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Thickness", "[", ".015", "]"}], ",", " ", "Purple", ",", 
          " ", 
          RowBox[{"Line", "[", 
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{
               RowBox[{"leftx", "+", ".01"}], ",", " ", "0"}], "}"}], ",", 
             " ", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"rightx", "-", ".01"}], ",", "0"}], "}"}]}], "}"}], 
           "]"}]}], "}"}], ",", " ", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Thickness", "[", ".015", "]"}], ",", " ", "Magenta", ",", 
          " ", 
          RowBox[{"Line", "[", 
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{"0", ",", " ", 
               RowBox[{
                RowBox[{"First", "[", 
                 RowBox[{"NMinimize", "[", 
                  RowBox[{
                   RowBox[{"{", 
                    RowBox[{
                    RowBox[{"f", "[", "x", "]"}], ",", " ", 
                    RowBox[{
                    "leftx", "\[LessEqual]", "x", "\[LessEqual]", 
                    "rightx"}]}], "}"}], ",", " ", "x"}], "]"}], "]"}], "+", 
                ".01"}]}], "}"}], ",", " ", 
             RowBox[{"{", 
              RowBox[{"0", ",", " ", 
               RowBox[{
                RowBox[{"First", "[", 
                 RowBox[{"NMaximize", "[", 
                  RowBox[{
                   RowBox[{"{", 
                    RowBox[{
                    RowBox[{"f", "[", "x", "]"}], ",", " ", 
                    RowBox[{
                    "leftx", "\[LessEqual]", "x", "\[LessEqual]", " ", 
                    "rightx"}]}], "}"}], ",", "x"}], "]"}], "]"}], "-", 
                ".01"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"ColorData", "[", "\"\<Crayola\>\"", "]"}], "[", 
           "\"\<BlueGray\>\"", "]"}], ",", " ", 
          RowBox[{"Opacity", "[", ".5", "]"}], ",", " ", 
          RowBox[{"Rectangle", "[", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{"Min", "[", 
               RowBox[{"leftx", ",", "0"}], "]"}], ",", " ", 
              RowBox[{"First", "[", 
               RowBox[{"NMinimize", "[", 
                RowBox[{
                 RowBox[{"{", 
                  RowBox[{
                   RowBox[{"f", "[", "x", "]"}], ",", " ", 
                   RowBox[{
                   "leftx", "\[LessEqual]", "x", "\[LessEqual]", "rightx"}]}],
                   "}"}], ",", " ", "x"}], "]"}], "]"}]}], "}"}], ",", " ", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"Max", "[", 
               RowBox[{"0", ",", "rightx"}], "]"}], ",", " ", 
              RowBox[{"First", "[", 
               RowBox[{"NMaximize", "[", 
                RowBox[{
                 RowBox[{"{", 
                  RowBox[{
                   RowBox[{"f", "[", "x", "]"}], ",", " ", 
                   RowBox[{
                   "leftx", "\[LessEqual]", "x", "\[LessEqual]", " ", 
                    "rightx"}]}], "}"}], ",", "x"}], "]"}], "]"}]}], "}"}]}], 
           "]"}]}], "}"}]}], "}"}]}]}], "]"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"leftx", ",", " ", "xmin", ",", " ", 
     RowBox[{"rightx", "-", ".1"}]}], "}"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"rightx", ",", "xmax"}], "}"}], ",", 
     RowBox[{"leftx", "+", ".1"}], ",", " ", "xmax"}], "}"}]}], 
  "]"}]}], "Input",
 CellChangeTimes->CompressedData["
1:eJwdyk0ogwEAh/E3c0CslcNM2GYstSLb7KAoTZLLNvIxYbbMt7iMXBCjZQqj
JZPvNkMOEpNMY8tHiThgvdiB0lyQN1Li/e/w9Ls8fF17sT6MIAgeHawaEOx4
LMG8ij7CBY1Zm/uwxmf0QMKmPIO14/Jz6GJRjzDilPUMt7vj3qBuyf8OO4fM
7ENaRUOAD5tEqTJoIg25sF75IYfH3PsCeMu0K6C3i6OGVHpfNWz+XdbAEUt0
I+ztqjPAqNhRC5xvFU7An1KODZKO1Rk41bb3A7/JVtYR7a5NnQDFmdokaE0t
EUJ2rz5kGdMkhmF3UgmcJcunb2jjvV82OCaYXIAdOTI7PMmv9sBCqd0HkwLZ
fnhBaR/glGb1CZqSe17gpUryButehim48udg3NIq2aJwGGPWRcBK/UMk5LvN
XOgyZPAgtS5NgdYJd8ihK90ijD5Yc4a+hJoNOMdwbsEKc9AFP8m0Q6gRJqp+
+1/zAtdFIVtE2WXQujyohv/WvB8T
  "]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{950, 773},
WindowMargins->{{185, Automatic}, {Automatic, 2}},
FrontEndVersion->"11.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \
21, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 124, 2, 92, "Title"],
Cell[706, 26, 153, 4, 49, "Subsubtitle"],
Cell[862, 32, 1241, 30, 106, "Text"],
Cell[2106, 64, 144, 2, 30, "Text"],
Cell[2253, 68, 1962, 55, 159, "Input"],
Cell[4218, 125, 142, 2, 30, "Text"],
Cell[4363, 129, 1720, 50, 159, "Input"],
Cell[6086, 181, 305, 7, 30, "Text"],
Cell[6394, 190, 3277, 94, 195, "Input"],
Cell[CellGroupData[{
Cell[9696, 288, 206, 2, 51, "Subtitle"],
Cell[9905, 292, 1054, 24, 68, "Text"],
Cell[10962, 318, 5488, 146, 306, "Input"]
}, Open  ]]
}, Open  ]]
}
]
*)