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<Startup-Code startupcode="plots:-setoptions( 'labels' = [''x'', ''y''],\012        'font' = [&quot;Times New Roman&quot;, 12],\012        'thickness' = 2 ):\012\012# Deal with problem that 'symbolsize' is a relative measure\012symbolsizefix := proc( plt, n::integer, norm::integer := 400 )\012        return round( n*norm/min( DocumentTools:-GetProperty( plt, 'pixelHeight' ),\012                DocumentTools:-GetProperty( plt, 'pixelWidth' ) ) );\012end proc; # symbolsizefix\012\012\012M4_5_2a := module()\012    export\012        Click,\012        Drag,\012        EndDrag,\012        Clear,\012        Invert;\012\012    local\012        GetIntervals,\012        DoPlot,\012        points,\012        farx,\012        fary,\012        new,\012        colourA,\012        colourB,\012        intervalsx,\012        intervalsy,\012        ToIntervals,\012        outside,\012        surrounding;\012\012    uses DT = DocumentTools;\012    points := [];\012    new := true;\012    colourA := &quot;DarkGreen&quot;;\012    colourB := &quot;Magenta&quot;;\012    intervalsx := [];\012    intervalsy := [];\012\012    outside := ( x, ints ) -&gt; andmap( a -&gt; x &lt; a[1] or x &gt; a[2], ints );\012    surrounding := ( x, far, ints ) -&gt; ormap( a -&gt; `if`( a[1] = a[2], x &lt; a[1] and far &gt; a[2] or\012            x &gt; a[2] and far &lt; a[1], x &lt;= a[1] and far &gt;= a[2] or x &gt;= a[2] and far &lt;= a[1] ), ints );\012\012    Click := proc()\012        local x, y;\012\012        DT:-Do( x = %Plot0( &quot;clickx&quot; ) );\012        DT:-Do( y = %Plot0( &quot;clicky&quot; ) );\012        intervalsx := ToIntervals( map( x -&gt; x[1], points ) );\012        intervalsy := ToIntervals( map( x -&gt; x[2], points ) );\012\012        if outside( x, intervalsx ) and outside( y, intervalsy )  then\012            points := [op( points ), [x, y], [undefined, undefined]];\012            DoPlot();\012            farx := x;\012            fary := y;\012            new := false;\012        end if;\012\012        DT:-Do( %Button3( &quot;enabled&quot; ) = true );\012\012        return NULL;\012    end proc; # Click\012\012\012    Drag := proc()\012        local x, y;\012\012        DT:-Do( x = %Plot0( &quot;endx&quot; ) );\012        DT:-Do( y = %Plot0( &quot;endy&quot; ) );\012        intervalsx := ToIntervals( map( x -&gt; x[1], points ) );\012        intervalsy := ToIntervals( map( x -&gt; x[2], points ) );\012\012        if outside( x, intervalsx ) and outside( y, intervalsy ) then\012            if new or not (surrounding( x, farx, intervalsx ) or surrounding( y, fary, intervalsy )) then\012                points := [op( points ), [x, y]];\012\012            else\012                points := [op( points ), [undefined, undefined], [x, y]];\012            end if;\012\012            DoPlot();\012            farx := x;\012            fary := y;\012            new := false;\012        end if;\012\012        DT:-Do( %Button3( &quot;enabled&quot; ) = true );\012\012        return NULL;\012    end proc; # Drag\012\012\012    EndDrag := proc()\012        points := [op( points ), [undefined, undefined]];\012    end proc; # EndDrag\012\012\012    Clear := proc()\012        points := [];\012        new := true;\012        DT:-Do( %Plot0 = plots:-pointplot( [], 'view' = [-10..10, -10..10], 'title' = &quot;Domain and Range&quot; ) );\012        colourA := &quot;DarkGreen&quot;;\012        colourB := &quot;Magenta&quot;;\012        DT:-Do( %Button3( &quot;enabled&quot; ) = false );\012        return NULL;\012    end proc; # Clear\012\012\012    Invert := proc()\012        points := map( x -&gt; [x[2], x[1]], points );\012        colourA, colourB := colourB, colourA;\012        DoPlot();\012        return NULL;\012    end proc; # Invert\012\012\012    DoPlot := proc()\012        local xInts, yInts, singletons;\012\012        xInts := GetIntervals( op~( 1, points ), 0 );\012        yInts := GetIntervals( op~( 2, points ), 1 );\012\012        singletons := select( t -&gt; evalb( nops( t ) = 1 ),\012                        [ ListTools:-Split( t -&gt; type( t[1], undefined ), points ) ] );\012\012        DT:-Do( %Plot0 = plots:-display( [\012                op( plots:-pointplot~( xInts, 'colour' = colourA, 'style' = 'line', 'thickness' = 4 ) ),\012                op( plots:-pointplot~( yInts, 'colour' = colourB, 'style' = 'line', 'thickness' = 4 ) ),\012                plots:-pointplot( points, 'style' = 'line', 'colour' = 'red', 'thickness' = 2 ),\012                op( plots:-pointplot~( xInts, 'colour' = colourA, 'style' = 'point',\012                    'symbol' = 'solidcircle', 'symbolsize' = symbolsizefix( 'Plot0', 20 ) ) ),\012                op( plots:-pointplot~( yInts, 'colour' = colourB, 'style' = 'point',\012                    'symbol' = 'solidcircle', 'symbolsize' = symbolsizefix( 'Plot0', 20 ) ) ),\012                # singletons\012                `if`( singletons &lt;&gt; [], plots:-pointplot( op~( singletons ), 'style' = 'point',\012                        'colour' = 'red', 'symbol' = 'solidbox', 'symbolsize' = symbolsizefix( 'Plot0', 14 ) ),\012                        NULL )\012                ],\012                'title' = &quot;Dom\303\255nio, Imagem, e Inversa&quot;,\012                'view' = [-10 .. 10, -10 .. 10]\012                ) );\012\012        return NULL;\012    end proc; # DoPlot\012\012\012    GetIntervals := proc( L0, selector )\012        local L, i;\012\012        L := subs( [] = NULL, [ ListTools:-Split( type, L0, undefined ) ] );\012\012        if selector = 0 then\012            return map( t -&gt; [ [t[1], 0], [t[-1], 0] ], L );\012\012        else\012            # intervals can overlap and be out of order on y axis, so sort (both\012            # interval endpoints and intervals themselves) and merge\012            L := sort( sort~( L ), ( a, b ) -&gt; evalb( a[1] &lt;= b[1] ) );\012\012            i := 1;\012\012            while i &lt; nops( L ) do\012                if L[i, -1] &gt;= L[i+1, 1] then\012                    L := subs( L[i] = [min( L[i, 1], L[i+1, 1] ), max( L[i, -1], L[i+1, -1] )],\012                            L[i+1] = NULL, L );\012\012                else\012                    i := i + 1;\012                end if;\012            end do;\012\012            return map( t -&gt; [ [0, t[1]], [0, t[-1]] ], L );\012        end if;\012    end proc; # GetIntervals\012\012\012    ToIntervals := L -&gt; map( x -&gt; `if`( nops( x ) &gt; 0, [min( x[1], x[-1] ), max( x[1], x[-1] )], NULL ),\012            [ListTools:-Split( type, L, 'undefined' )] );\012\012end module; # M4_5_2a\012\012\012M4_5_2b := module()\012    export\012        Click,\012        Drag,\012        EndDrag,\012        SelChange,\012        Toggle,\012        Clear;\012    local\012        DoPlot,\012        FTable,\012        CurFunc,\012        Reset,\012        Inverted,\012        FList,\012        Times,\012        Update,\012        StartTime,\012        EndTime,\012        Pts,\012        Distance,\012        Distance2,\012        EndPoint,\012        Bound,\012        Func,\012        Radius,\012        Accuracy;\012\012    uses DT = DocumentTools;\012\012    FTable := table(\012            [\012            &quot;sin(x)&quot; = [sin, [-10, 10], [-Pi, Pi],0],\012            &quot;ln(x)&quot; = [ln, [exp( -10 ), 10], [-10, 10],0],\012            &quot;x^2&quot; = [x -&gt; x^2, [-sqrt( 10 ), sqrt( 10 )], [-5, 5],0.0],\012            &quot;x^3/27&quot; = [x -&gt; ( x/3 )^3, [3*( -10^( 1/3 ) ), 3*( 10^( 1/3 ) )], [-6, 6],0.0],\012            &quot;sin(3*x)+cos(2*x)&quot; = [x -&gt; sin( 3*x )+cos( 2*x ), [-10, 10], [-5, 5],0],\012            &quot;sqrt(25-x^2)&quot; = [x -&gt; sqrt( 25-x^2 ), [-5, 5], [-10, 10],0.0]\012            ]\012            );\012    FList := sort( [indices( FTable, 'nolist' )] );\012\012    Inverted := false;\012\012    StartTime := NULL;\012    EndTime := NULL;\012    Pts := [];\012    Times := [];\012    Radius := 0.75;\012    Reset := true;\012    Inverted := false;\012\012    DT:-Do( %ComboBox0( &quot;itemList&quot; ) = FList );\012    DT:-Do( %CheckBox0 = Inverted );\012    DT:-Do( %ComboBox0( &quot;value&quot; ) = FList[1] );\012\012\012    Click := proc()\012        Pts := [];\012        StartTime := NULL;\012        EndTime := NULL;\012        Update();\012        DoPlot();\012    end proc; # Click\012\012\012    Drag := proc()\012        local x, y, d1, d2;\012\012        DT:-Do( x = %Plot1( &quot;endx&quot; ) );\012        DT:-Do( y = %Plot1( &quot;endy&quot; ) +  FTable[CurFunc][4] );\012\012        if Inverted then\012            ( x, y ) := ( y, x );\012        end if;\012\012        if EndTime &lt;&gt; NULL or Reset &lt;&gt; true then\012            return;\012        end if;\012\012        if StartTime = NULL then\012            d1 := Distance( [x, y], [Bound[1], Func( Bound[1] )] );\012            d2 := Distance( [x, y], [Bound[2], Func( Bound[2] )] );\012\012            if d1 &lt; Radius or d2 &lt; Radius then\012                StartTime := time[real]();\012                Pts := [[x, y]];\012                EndPoint := `if`( d1 &gt; d2, Bound[1], Bound[2] );\012            end if;\012\012        else\012            if evalf( Distance( [x, y], [EndPoint, Func( EndPoint )] ) ) &lt; Radius then\012                EndTime := time[real]();\012                Pts := [op( Pts ), [x, y]];\012                DT:-SetProperty( 'TextArea0', 'value', cat( op( map( convert, ( map( x -&gt; (\012                    &quot;Function: &quot;,\012                    x[3],\012                    &quot;\134nInverted Tracing: &quot;,\012                    `if`( x[2] = true, &quot;On&quot;, &quot;Off&quot; ),\012                    &quot;\134nTime: &quot;,\012                    x[1],\012                    &quot;\134nAccuracy: &quot;,\012                    x[4],\012                    &quot;\134n&quot; ),\012                    Times ),\012                'string' ) ) ), &quot;\134n...Gravando novo tempo...&quot; ), 'refresh' = true );\012                DoPlot();\012                Times := [op( Times ), [EndTime-StartTime, Inverted, CurFunc, Accuracy()]];\012                Update();\012                StartTime := NULL;\012                EndTime := NULL;\012                Reset := false;\012\012            else\012                Pts := [op( Pts ), [x, y]];\012            end if;\012        end if;\012\012        Update();\012        DoPlot();\012    end proc; # Drag\012\012\012    EndDrag := proc()\012        Reset := true;\012    end proc; # EndDrag\012\012\012    SelChange := proc()\012        # Use GetProperty so we don't try to parse\012        CurFunc := DT:-GetProperty( 'ComboBox0', 'value' );\012        Func := FTable[CurFunc][1];\012        Bound := FTable[CurFunc][2];\012        Pts := [];\012        StartTime := NULL;\012        EndTime := NULL;\012        Update();\012        DoPlot();\012        Clear();\012    end proc; # SelChange\012\012\012    Toggle := proc()\012        Inverted := not Inverted;\012        StartTime := NULL;\012        EndTime := NULL;\012        Pts := [];\012        DoPlot();\012    end proc; # Toggle\012\012\012    Clear := proc()\012        Times := [];\012        Update();\012    end proc; # Clear\012\012\012    DoPlot := proc()\012        local x, y;\012\012        DT:-Do( %Plot1 = plots:-display(\012            [\012            plots:-pointplot( Pts, 'style' = 'line' ),\012            plot( FTable[CurFunc][1] ),\012            plots:-pointplot(\012                map( x -&gt; `if`( Inverted, [FTable[CurFunc][1]( x ), x], [x, FTable[CurFunc][1]( x )] ),\012                    FTable[CurFunc][2] ),\012                'style' = 'point',\012                'symbol' = 'solidcircle',\012                'colour' = &quot;DarkGreen&quot;,\012                'symbolsize' = symbolsizefix( 'Plot0', 20 )\012                )\012            ],\012            'view' = [-10..10, -10..10],\012            'title' = typeset( &quot;Gr\303\241fico de &quot;, y = Func( x ), `if`( Inverted, &quot;: Tra\303\247ado Invertido&quot;, NULL ))\012            ) );\012        return NULL;\012    end proc; # DoPlot\012\012\012    Update := proc()\012        DT:-Do( %TextArea0 = cat( &quot;&quot;, op( map( convert, ( map( x -&gt; (\012                &quot;\134nTra\303\247ado Invertido: &quot;,\012                `if`( x[2] = true, &quot;On&quot;, &quot;Off&quot; ),\012                &quot;\134nTempo: &quot;,\012                x[1],\012                &quot;\134nAcur\303\241cia: &quot;,\012                x[4],\012                &quot;\134n&quot;,\012                &quot;_____________________\134n&quot; ),\012                Times ),\012                'string' ) ) ) ) );\012        return NULL;\012    end proc; # Update\012\012\012    Distance := ( x, y ) -&gt; evalf( sqrt( (x[1]-y[1])^2 + (x[2]-y[2])^2 ) );\012\012\012    Distance2 := proc( f, p, r )\012        local n, x;\012        n := [fsolve( diff( f( x ), x ) * (f( x )-p[2]) + x - p[1], x = p[1]+r[1] .. p[1]+r[2] )];\012        n := [`if`( type( n, 'list'( 'numeric' ) ), op( n ), NULL ), FTable[CurFunc][2][1],\012                FTable[CurFunc][2][2]];\012        return min( map( a -&gt; Distance( [a, f(a)], p ), n ) );\012    end proc;\012\012\012    Accuracy := proc()\012        local raw;\012\012        raw := 100.0 - 100.0*Statistics:-Mean( map2( Distance2, Func, Pts, FTable[CurFunc][3] ) );\012        return max( 1, round( .1 * raw ) );\012    end proc; # Accuracy\012\012end module; # M4_5_2b\012\012\012# Initialize components\012proc()\012    local x, y, f;\012    uses DT = DocumentTools;\012\012    DT:-Do( %Button3( &quot;enabled&quot; ) = false );\012    M4_5_2b:-SelChange();\012    return NULL;\012end proc();\012\012\012"/>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">O espelho reflete de frente para tr\303\241s. A interpreta\303\247\303\243o de esquerda e direita vem sendo revertido a partir de sua mente que imagina o seu corpo na posi\303\247\303\243o do seu reflexo. A maneira mais simples para a sua mente para fazer isto \303\251 imaginar um giro de 180 \302\260 em torno do eixo vertical. Se os nossos olhos estavesem  alinhados horizontalmente e n\303\243o verticalmente, ver\303\255amos o nosso reflexo  nos espelhado de cabe\303\247a para baixo?</Font></Text-field>
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<Input><Text-field style="Text" layout="Title" alignment="left"><Font encoding="UTF-8">Nesta apresenta\303\247\303\243o,Vamos considerar os conceitos  <Font italic="true">dom\303\255nio de uma fun\303\247\303\243o inversa e</Font></Font> o  <Font encoding="UTF-8" italic="true">iimagem de uma fun\303\247\303\243o inversa</Font>.</Text-field>
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<Input><Text-field style="Text" layout="Title" alignment="left"><Font encoding="UTF-8">Vamos considerar que voc\303\252 j\303\241 esteja familiarizado com esses termos adicionais,que s\303\243o definidos em outras apresenta\303\247\303\265es desta cole\303\247\303\243o: <Font italic="true">fun\303\247\303\243o</Font></Font>, <Font encoding="UTF-8" italic="true">dom\303\255nio</Font>, <Font italic="true">imagem</Font>,<Font italic="true"> teste da reta vertical,</Font> <Font italic="true">teste da reta horizontal</Font>, e <Font encoding="UTF-8" italic="true">fun\303\247\303\243o por partes</Font>.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Para determinar algebricamente a formula de uma fun\303\247\303\243o inversa de  </Font><Equation executable="false" style="2D Math" input-equation="" 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encoding="UTF-8">. Mudar os pap\303\251is de </Font><Font italic="true">Y e X </Font><Font encoding="UTF-8">efetivamente troca as fun\303\247\303\265es do <Font italic="true">dom\303\255nio e imagem</Font></Font> de <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=</Equation>.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Supondo que voc\303\252 tenha uma fun\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=</Equation><Font encoding="UTF-8"> cuja a inversa \303\251 </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>. Em seguida o  <Font bold="true" encoding="UTF-8">dom\303\255nio da fun\303\247\303\243o inversa</Font> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> \303\251 o intervalo de  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=</Equation> e o <Font bold="true" encoding="UTF-8">imagem da fun\303\247\303\243o inversa</Font> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> \303\251 o dom\303\255nio de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=</Equation>.</Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Demonstra\303\247\303\243o</Font></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Desenhar uma fun\303\247\303\243o invers\303\255vel no gr\303\241fico. </Font></Text-field><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Enquanto voc\303\252 desenha, o dom\303\255nio e o alcance de sua fun\303\247\303\243o ser\303\241 mostrada no </Font><Font italic="true">x</Font>- e <Font italic="true">y</Font>-axes.</Text-field>
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<Input><Text-field style="Text" layout="Normal">Clique <Font bold="true">Limpar</Font><Font encoding="UTF-8"> para come\303\247ar novamente.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Clique <Font bold="true">Inverter</Font><Font encoding="UTF-8"> para tra\303\247ar o inverso de sua fun\303\247\303\243o.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">No in\303\255cio de 1900, Ivo Kohler, um psic\303\263logo austr\303\255aco, realizou experimentos para testar a capacidade de adapta\303\247\303\243o da percep\303\247\303\243o humana. Ele usou um par de \303\263culos com prismas em anexo, que teria invertido o que o usu\303\241rio v\303\252: at\303\251 torna-se para baixo e para baixo torna-se para cima. Inicialmente, os sujeitos (incluindo ele pr\303\263prio Kohler) tiveram uma grande dificuldade com tarefas simples, como comer ou andar, mas depois de v\303\241rios dias os seus c\303\251rebros adaptados \303\240 mudan\303\247a e eles foram capazes de funcionar quase normalmente (embora eles ainda estavam conscientes da distor\303\247\303\243o). Ao retirar os \303\263culos, eles experimentaram um efeito semelhante a quando primeiro coloc\303\241-los em: tarefas tornou-se dif\303\255cil voltar para o seu c\303\251rebro adaptado (embora eles n\303\243o percebem qualquer deforma\303\247\303\243o).</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">No exemplo abaixo, escolha uma fun\303\247\303\243o na lista de </Font><Font bold="true">F<Font encoding="UTF-8">un\303\247\303\243o Sele\303\247\303\243o</Font></Font><Font encoding="UTF-8">. Depois, tente tra\303\247ar o gr\303\241fico da fun\303\247\303\243o (a partir de um ponto verde para o outro). Seu tempo e outras informa\303\247\303\265es relevantes ser\303\243o exibidos \303\240 direita. Em seguida, selecione a caixa de sele\303\247\303\243o </Font><Font bold="true">Inverter</Font><Font encoding="UTF-8"> e tenta tra\303\247ar o gr\303\241fico novamente (os pontos verdes servem para indicar o in\303\255cio e t\303\251rmino posi\303\247\303\265es). Com </Font><Font bold="true">Inverter</Font><Font encoding="UTF-8"> selecionada, a posi\303\247\303\243o vertical \303\251 interpretado como horizontal, vertical e horizontal. Veja como o seu tempo e comparar com precis\303\243o a invertida e n\303\243o invertida rastreamento. Para limpar a caixa \303\240 direita, clique em </Font><Font bold="true">Limpar</Font>.</Text-field>
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