(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 5404, 174] NotebookOptionsPosition[ 4984, 155] NotebookOutlinePosition[ 5345, 171] CellTagsIndexPosition[ 5302, 168] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Reciprocal Functions", "Title", CellChangeTimes->{{3.496182036704987*^9, 3.496182041719369*^9}}, TextAlignment->Center], Cell["\<\ by Ruth Dover Illinois Mathematics and Science Academy\ \>", "Subsubtitle", CellChangeTimes->{{3.692572963526102*^9, 3.692572975810774*^9}}], Cell[TextData[{ "An example is given below with \[Florin], ", StyleBox["xmin", FontSlant->"Italic"], ", ", StyleBox["xmax, ymin, ", FontSlant->"Italic"], "and ", StyleBox["ymax", FontSlant->"Italic"], ". Edit these as you wish and then use shift-enter to execute the command. \ The graphs of ", StyleBox["y", FontSlant->"Italic"], " = \[Florin](", StyleBox["x", FontSlant->"Italic"], ") and ", StyleBox["y", FontSlant->"Italic"], " = 1/\[Florin](", StyleBox["x", FontSlant->"Italic"], ") are shown along with ", StyleBox["y", FontSlant->"Italic"], " = 1 and ", StyleBox["y", FontSlant->"Italic"], " = -1 to help see where the graphs of the reciprocals intersect. " }], "Text", CellChangeTimes->{{3.496182182002501*^9, 3.496182248019608*^9}, { 3.4961835768329687`*^9, 3.4961836094639807`*^9}, {3.496183854909254*^9, 3.4961838709642677`*^9}, {3.496349420051803*^9, 3.496349524169715*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{ SuperscriptBox["x", "2"], "-", "4"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"xmin", "=", RowBox[{"-", "5"}]}], ";", " ", RowBox[{"xmax", " ", "=", " ", "5"}], ";", " ", RowBox[{"ymin", "=", RowBox[{"-", "6"}]}], ";", " ", RowBox[{"ymax", "=", "6"}], ";"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Please", " ", "leave", " ", "the", " ", "rest", " ", "of", " ", "the", " ", "coding", " ", RowBox[{"alone", "!"}]}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", " ", RowBox[{"1", "/", RowBox[{"f", "[", "x", "]"}]}], ",", " ", "1", ",", " ", RowBox[{"-", "1"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "xmin", ",", " ", "xmax"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"ymin", ",", " ", "ymax"}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Thick", ",", " ", "Thick", ",", " ", "Gray", ",", " ", "Gray"}], "}"}]}], ",", " ", RowBox[{"Exclusions", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Numerator", "[", RowBox[{"f", "[", "x", "]"}], "]"}], "\[Equal]", "0"}], ",", " ", RowBox[{ RowBox[{"Denominator", "[", RowBox[{"f", "[", "x", "]"}], "]"}], "\[Equal]", "0"}]}], "}"}]}], ",", " ", RowBox[{"ExclusionsStyle", "\[Rule]", "Dashed"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"StringForm", "[", RowBox[{"\"\<\[Florin](\!\(\* StyleBox[\"x\", FontSlant->\"Italic\"]\)) = ``, \>\"", ",", " ", RowBox[{"f", "[", "x", "]"}]}], "]"}], ",", " ", RowBox[{"FontColor", "->", "Blue"}], ",", " ", RowBox[{"FontSize", "\[Rule]", "16"}]}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ RowBox[{"StringForm", "[", StyleBox[ RowBox[{" ", StyleBox[" ", FontColor->GrayLevel[0]]}]], RowBox[{ StyleBox["\"\<1/\[Florin](\!\(\* StyleBox[\"x\", FontSlant->\"Italic\"]\)) = ``\>\"", FontColor->GrayLevel[0]], ",", " ", RowBox[{"1", "/", RowBox[{"f", "[", "x", "]"}]}]}], "]"}], ",", " ", RowBox[{"FontColor", "\[Rule]", "Brown"}], ",", RowBox[{"FontSize", "\[Rule]", "16"}]}], "]"}]}], "}"}], "]"}]}]}], "]"}]}], "Input", CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGCQAmIQPTM8R7WA55Vjva+0MYh+5a3jCqJfmu/1ANFGe976 gWjxxrIYEK3D5FkNotnVjjaAaNMaifkgWmAB+0IQzRv0dBuIjozt3AGit7vK 7gPRiU6TLoDp7pTrIPpd5Q8wneXMfQ9E163ueACiC8o+vAHRH/apvAXRHYpZ P0H0Pp+EvyD61L71tw4C6SDe72D6xenrr0H0spXp70E0x/zfTIeAtJqTkgCI PhW6SwRET62fLwei3fUE3x8G0nphtz+C6F+b934D0ULsyd9BtP2OLoUjQLpn f54SiP6waK4WiK6bnqUDohc3+xmD6ELt6aYgmn9WnSWI/n9OyAZEy69V8gLR lcImYNppZkEIiPa9tQVMZ9i7pIPoF/LXwbRKh5NFKtdrx8tnY8C0w4Jt6mzN rx0jA5Q1QDQAvGzCNQ== "]] }, Open ]] }, WindowSize->{640, 708}, WindowMargins->{{873, Automatic}, {Automatic, 121}}, 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[567, 22, 127, 2, 92, "Title"], Cell[697, 26, 151, 4, 49, "Subsubtitle"], Cell[851, 32, 932, 33, 87, "Text"], Cell[1786, 67, 3182, 85, 243, "Input"] }, Open ]] } ] *)