1500
[ randRange( -9, -1 ), randRange( 1, 9 ) ]
(function() {
var functionPath = [];
var prev;
var push = function( val ) {
prev = val;
functionPath.push( prev );
};
push([ DOMAIN[0], randRange( -5, 5 ) ]);
for( var i = DOMAIN[0]+1; i <= DOMAIN[1]; i++ ) {
if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] < 8 ) {
push([i, prev[1]+1]);
} else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] > -8 ) {
push([i, prev[1]-1]);
} else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] < 7 ) {
push([i, prev[1]+2]);
} else if ( abs( randRangeNonZero( -10, 10 ) < 3 ) && prev[1] > -7 ) {
push([i, prev[1]-2]);
} else {
push([i, prev[1]]);
}
}
return functionPath;
})()
(function() {
var values = $.map( FUNCTION_PATH, function( p ) { return p[1]; } );
return [ min.apply( null, values ), max.apply( null, values ) ];
})()
Der Graph der Funktion f ist dargestellt.
graphInit({
range: 10,
scale: 20,
tickStep: 1,
labelStep: 1,
unityLabels: false,
labelFormat: function( s ) { return "\\small{" + s + "}"; }
});
label( [ -0.5, 9.5 ], "{f(x)}", "left" );
label( [ 9, 0.75 ], "x", "right" );
graph.fn_path = path( FUNCTION_PATH, { stroke: BLUE } );
circle( FUNCTION_PATH[0], 0.15, { stroke: "none", fill: BLUE } );
circle( FUNCTION_PATH[ FUNCTION_PATH.length - 1], 0.15, { stroke: "none", fill: BLUE } );
Was ist der Definitionsbereich?
untere Grenze:
untere Grenze:
DOMAIN[0]
obere Grenze:
obere Grenze:
DOMAIN[1]
Für welche Werte von x existieren Werte f(x)?
Auf der x-Achse als Zahlengerade sehen wir:
var domain_path = graph.fn_path.clone();
var tmp_path = path( $.map( FUNCTION_PATH, function( p ) { return [[ p[0], 0 ]]; }), { stroke: "none" } );
domain_path.animate( { path: tmp_path.attrs.path, "stroke-width": 4, stroke: GREEN }, ANIM_SPEED, "ease-in-out");
circle( [ FUNCTION_PATH[0][0], 0 ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } )
.animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" );
circle( [ FUNCTION_PATH[ FUNCTION_PATH.length - 1 ][0], 0 ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } )
.animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" );
tmp_path.remove();
für den Definitionsbereich: DOMAIN[0]\le x\le DOMAIN[1],
d.h. die untere Grenze ist DOMAIN[0] und die obere Grenze beträgt DOMAIN[1].