Difference between revisions of "Rational functions"

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Line 27: Line 27:
 
         p[1] = board.createElement('point', [3,-1], {style:6});
 
         p[1] = board.createElement('point', [3,-1], {style:6});
 
         var f = board.lagrangePolynomial(p);
 
         var f = board.lagrangePolynomial(p);
         graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});
+
         graph = board.createElement('functiongraph', [f,-10, 10]);
  
 
         function addPoint1() {
 
         function addPoint1() {
Line 42: Line 42:
 
         q[1] = board2.createElement('point', [3,-1], {style:6});
 
         q[1] = board2.createElement('point', [3,-1], {style:6});
 
         var f2 = board2.lagrangePolynomial(q);
 
         var f2 = board2.lagrangePolynomial(q);
         graph2 = board2.createElement('curve', ['x', f2, 'x', -10, 10], {curveType:'graph'});
+
         graph2 = board2.createElement('functiongraph', [f2, -10, 10]);
  
 
         function addPoint2() {
 
         function addPoint2() {
Line 53: Line 53:
 
         b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
 
         b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
 
         b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
 
         b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
         graph3 = board3.createElement('curve', ['x', function(x){return f(x)/f2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'});
+
         graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
 
            
 
            
 
</script>
 
</script>
Line 65: Line 65:
 
<source lang="javascript">
 
<source lang="javascript">
 
         board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
 
         board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
         board.createElement('axis', [[0,0], [1,0]]);
+
         // Axes
         board.createElement('axis', [[0,0], [0,1]]);
+
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 +
         b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
  
 
         var p = [];
 
         var p = [];
Line 73: Line 74:
 
         p[1] = board.createElement('point', [3,-1], {style:6});
 
         p[1] = board.createElement('point', [3,-1], {style:6});
 
         var f = board.lagrangePolynomial(p);
 
         var f = board.lagrangePolynomial(p);
         graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});
+
         graph = board.createElement('functiongraph', [f,-10, 10]);
  
 
         function addPoint1() {
 
         function addPoint1() {
Line 81: Line 82:
  
 
         board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
 
         board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
         board2.createElement('axis', [[0,0], [1,0]]);
+
         // Axes
         board2.createElement('axis', [[0,0], [0,1]]);
+
        b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
 +
         b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});
  
 
         q[0] = board2.createElement('point', [-1,2], {style:6});
 
         q[0] = board2.createElement('point', [-1,2], {style:6});
 
         q[1] = board2.createElement('point', [3,-1], {style:6});
 
         q[1] = board2.createElement('point', [3,-1], {style:6});
 
         var f2 = board2.lagrangePolynomial(q);
 
         var f2 = board2.lagrangePolynomial(q);
         graph2 = board2.createElement('curve', ['x', f2, 'x', -10, 10], {curveType:'graph'});
+
         graph2 = board2.createElement('functiongraph', [f2, -10, 10]);
  
 
         function addPoint2() {
 
         function addPoint2() {
Line 95: Line 97:
  
 
         board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
 
         board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
         board3.createElement('axis', [[0,0], [1,0]]);
+
         // Axes
         board3.createElement('axis', [[0,0], [0,1]]);
+
        b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
         board3.createElement('curve', ['x', function(x){return f(x)/f2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'});
+
         b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
 +
         graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Revision as of 13:08, 10 March 2009

Polynomial [math]f[/math]:

Polynomial [math]g[/math]:

Rational function [math]\frac{f}{g}[/math]:

References

The underlying JavaScript source code

        board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

        var p = [];
        var q = [];
        p[0] = board.createElement('point', [-1,2], {style:6});
        p[1] = board.createElement('point', [3,-1], {style:6});
        var f = board.lagrangePolynomial(p);
        graph = board.createElement('functiongraph', [f,-10, 10]);

        function addPoint1() {
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board.update();
        }

        board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
        b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});

        q[0] = board2.createElement('point', [-1,2], {style:6});
        q[1] = board2.createElement('point', [3,-1], {style:6});
        var f2 = board2.lagrangePolynomial(q);
        graph2 = board2.createElement('functiongraph', [f2, -10, 10]);

        function addPoint2() {
          q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board2.update();
        }

        board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
        // Axes
        b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
        b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
        graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});