Draggable exponential function: Difference between revisions

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Plot the function
Plot the function
$$y = e^{ax}$$
:<math> y = e^{ax}</math>
where the parameter ''a'' is determined by the Point ''A=(x_A, x_Y)''.
where the parameter <math>a</math> is determined by the Point <math>A=(x_A, y_A)</math>.
 
That means,
:<math> a = log(y_A) / x_A </math>
 
<jsxgraph width="400" height="400" box="box1">
<jsxgraph width="400" height="400" box="box1">
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 20, 5, -1], axis:true});
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 20, 5, -1], axis:true});


var p = board.create('point', [1, Math.exp(1)]);
var A = board.create('point', [1, Math.exp(1)]);
var graph = board.create('functiongraph', [
var graph = board.create('functiongraph', [
         function(x) {
         function(x) {
             var a = Math.log(p.Y()) / p.X();
             var a = Math.log(A.Y()) / A.X();
             return Math.exp(a * x);
             return Math.exp(a * x);
         }]);
         }]);
            
            
var txt = board.create('text', [-3, 10, function () {
var txt = board.create('text', [-3, 10, function () {
           return "a = " + (Math.log(p.Y()) / p.X()).toFixed(2);
           return "a = " + (Math.log(p.Y()) / A.X()).toFixed(2);
           }], {fontSize: 16});
           }], {fontSize: 16});
</jsxgraph>
</jsxgraph>
Line 22: Line 26:
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 20, 5, -1], axis:true});
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 20, 5, -1], axis:true});


var p = board.create('point', [1, Math.exp(1)]);
var A = board.create('point', [1, Math.exp(1)]);
var graph = board.create('functiongraph', [
var graph = board.create('functiongraph', [
         function(x) {
         function(x) {
             var a = Math.log(p.Y()) / p.X();
             var a = Math.log(A.Y()) / A.X();
             return Math.exp(a * x);
             return Math.exp(a * x);
         }]);
         }]);
            
            
var txt = board.create('text', [-3, 10, function () {
var txt = board.create('text', [-3, 10, function () {
           return "a = " + (Math.log(p.Y()) / p.X()).toFixed(2);
           return "a = " + (Math.log(p.Y()) / A.X()).toFixed(2);
           }], {fontSize: 16});
           }], {fontSize: 16});
</source>
</source>

Revision as of 09:35, 16 February 2016

Plot the function

[math]\displaystyle{ y = e^{ax} }[/math]

where the parameter [math]\displaystyle{ a }[/math] is determined by the Point [math]\displaystyle{ A=(x_A, y_A) }[/math].

That means,

[math]\displaystyle{ a = log(y_A) / x_A }[/math]


The JavaScript code

var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 20, 5, -1], axis:true});

var A = board.create('point', [1, Math.exp(1)]);
var graph = board.create('functiongraph', [
         function(x) {
            var a = Math.log(A.Y()) / A.X();
            return Math.exp(a * x);
         }]);
           
var txt = board.create('text', [-3, 10, function () {
           return "a = " + (Math.log(p.Y()) / A.X()).toFixed(2);
          }], {fontSize: 16});