Begrepp

Funktion

En funktion är en omvandlingsregel. Man sätter in ett värde som via regeln (även kallat funktionsuttrycket) skapar ett nytt värde. Invärdet brukar kallas

x

(oberoende variabel) medan utvärdet brukar kallas

y

eller

f (x)

(beroende variabel).

Omvandlingsregeln här kan tolkas i ord som "addera 3". Utvärdet $y$ bildas alltså genom att addera 3 till invärdet $x .$ Paret av $x$ och $y$ kan tolkas som en punkt. Genom att räkna ut flera sådana punkter som funktionen bildar och sätta ut punkterna i ett koordinatsystem kan funktionen illustreras grafiskt. För att en regel ska få kallas en funktion får varje $x$ som mest ge ett $y$ -värde. Däremot får samma $y$ -värde återkomma för flera olika $x .$

@@ Rad 3: / Rad 3: @@
 <translate><!--T:13--> En funktion är en '''omvandlingsregel'''. Man sätter in ett värde som via regeln (även kallat [[Funktionsuttryck *Wordlist*|funktionsuttrycket]]) skapar ett nytt värde. Invärdet brukar kallas $x$<t3> ([[Oberoende variabel *Wordlist*|oberoende variabel]])</t3> medan utvärdet brukar kallas $y$ eller $f(x)$<t4> ([[Beroende variabel *Wordlist*|beroende variabel]])</t4>.</translate>
 <jsxgpre id="funkMaskin234">
-	var strings = {
+var strings = {
-      value: '<translate><!--T:11--> värde</translate>',
+	value: '<translate><!--T:11--> värde</translate>',
-      function: '<translate><!--T:12--> Funktion</translate>'
+	function: '<translate><!--T:12--> Funktion</translate>'
-    };
+};
-    var b = mlg.board([-0.5,1.7,7.5,-0.1],{grid:false, desktopSize:'medium'});
+var b = mlg.board([-0.5,1.7,7.5,-1.8],{grid:false, desktopSize:'medium'});
-    b.txt(0.5,1.4,'x'.italics() + " " + strings.value + ':',{fontSize:1.1, mathMode:false});
+b.txt(0.5,1.4,'x'.italics() + " " + strings.value + ':',{fontSize:1.1, mathMode:false});
-    b.polygon([[0,1.1],[1,1.1],[1,0.2],[0,0.2]],{vertices:{visible:false},fillColor:'lightyellow',layer:8});
+b.polygon([[0,1.1],[1,1.1],[1,0.2],[0,0.2]],{vertices:{visible:false},fillColor:'lightyellow',layer:8});
-    b.txt(6.5,1.4,'y'.italics() + " " + strings.value + ':',{fontSize:1.1, mathMode:false});
+b.txt(6.5,1.4,'y'.italics() + " " + strings.value + ':',{fontSize:1.1, mathMode:false});
-    b.polygon([[6,1.1],[7,1.1],[7,0.2],[6,0.2]],{vertices:{visible:false},fillColor:'lightyellow',layer:8});
+b.polygon([[6,1.1],[7,1.1],[7,0.2],[6,0.2]],{vertices:{visible:false},fillColor:'lightyellow',layer:8});
-    b.txt(3.5,1.4, strings.function + ':',{fontSize:1.1, mathMode:false});
+b.txt(3.5,1.4, strings.function + ':',{fontSize:1.1, mathMode:false});
-    var fatPoint1=b.node(2,1.1);
+var fatPoint1=b.node(2,1.1);
-    var fatPoint2=b.node(2,0.2);
+var fatPoint2=b.node(2,0.2);
-    b.polygon([[2,1.1],fatPoint1,[5,1.1],[5,0.2],fatPoint2,[2,0.2]],{vertices:{visible:false},fillColor:'#FAFCC4',layer:8});
+b.polygon([[2,1.1],fatPoint1,[5,1.1],[5,0.2],fatPoint2,[2,0.2]],{vertices:{visible:false},fillColor:'#FAFCC4',layer:8});
-    var funktion = b.txt(3.5,0.63,'f(x)=x+3',{fontSize:1.2});
+var funktion = b.txt(3.5,0.63,'f(x)=x+3',{fontSize:1.2});
-    var travel = b.txt(0.4,0.63,'x',{fontSize:1.2,color:'blue'});
+var travel = b.txt(0.4,0.63,'x',{fontSize:1.2,color:'blue'});
-    var xbox = b.txt(0.4,0.63,'x',{fontSize:1.2});
+var xbox = b.txt(0.4,0.63,'x',{fontSize:1.2});
-    b.curve([1,1.1,1.1,1.9,1.9,5.1,5.1,5.9,5.9,6,6,5.9,5.9,5.1,5.1,1.9,1.9,1.1,1.1,1],
+b.curve([1,1.1,1.1,1.9,1.9,5.1,5.1,5.9,5.9,6,6,5.9,5.9,5.1,5.1,1.9,1.9,1.1,1.1,1],
-        [0.3,0.3,0.4,0.4,0.3,0.3,0.4,0.4,0.3,0.3,1,1,0.9,0.9,1,1,0.9,0.9,1,1],{strokeColor:'black'});
+	[0.3,0.3,0.4,0.4,0.3,0.3,0.4,0.4,0.3,0.3,1,1,0.9,0.9,1,1,0.9,0.9,1,1],{strokeColor:'black'});
-    var ready=true;
+var ready=true;
-    var runAnimation = function(strings){
+var runAnimation = function(strings){
-        if(ready){
+	if(ready){
-            ready=false;
+ ready=false;
-            travel.setAttribute({transitionDuration:0,opacity:0});
+ travel.setAttribute({transitionDuration:0,opacity:0});
-            b.changeText(funktion,'f(x)=x+3');
+ b.changeText(funktion,'f(x)=x+3');
-            b.changeText(xbox,strings['x']);
+ b.changeText(xbox,strings['x']);
-            b.changeText(travel,strings['x']);
+ b.changeText(travel,strings['x']);
-            travel.setAttribute({color:'blue'});
+ travel.setAttribute({color:'blue'});
-            setTimeout(function(){b.show(travel);b.moveAlong(travel,[[0.5,0.63],[1.9,0.63]],1500);},1000);
+ setTimeout(function(){b.show(travel);b.moveAlong(travel,[[0.5,0.63],[1.9,0.63]],1500);},1000);
-            setTimeout(function(){b.hide(travel,200);
+ setTimeout(function(){b.hide(travel,200);
-                fatPoint1.moveTo([2.1,1.2]);
+ fatPoint1.moveTo([2.1,1.2]);
-                fatPoint2.moveTo([2.1,0.1]);
+ fatPoint2.moveTo([2.1,0.1]);
-                b.translate([fatPoint1,fatPoint2],2.9,null,1500);
+ b.translate([fatPoint1,fatPoint2],2.9,null,1500);
-            },2500);
+ },2500);
-            setTimeout(function() {b.changeText(funktion,'f(\\textcolor{blue}{'+strings['x']+'})=x+3');}, 3000);
+ setTimeout(function() {b.changeText(funktion,'f(\\textcolor{blue}{'+strings['x']+'})=x+3');}, 3000);
-            setTimeout(function() {b.changeText(funktion,'f(\\textcolor{blue}{'+strings['x']+'})=\\textcolor{blue}{'+strings['x']+'}+3');}, 3400);
+ setTimeout(function() {b.changeText(funktion,'f(\\textcolor{blue}{'+strings['x']+'})=\\textcolor{blue}{'+strings['x']+'}+3');}, 3400);
-            setTimeout(function(){fatPoint1.moveTo([2.1,1.1]);fatPoint2.moveTo([2.1,0.2]);b.changeText(travel,strings['y']);travel.setAttribute({color:'black'});travel.moveTo([5,0.6]);b.show(travel);b.moveAlong(travel,[[5,0.63],[6.4,0.63]],1500);},4100);
+ setTimeout(function(){fatPoint1.moveTo([2.1,1.1]);fatPoint2.moveTo([2.1,0.2]);b.changeText(travel,strings['y']);travel.setAttribute({color:'black'});travel.moveTo([5,0.6]);b.show(travel);b.moveAlong(travel,[[5,0.63],[6.4,0.63]],1500);},4100);
-            setTimeout(function(){ready=true;}, 5600);
+ setTimeout(function(){ready=true;}, 5600);
-        }
+	}
-    };
+};
-    mlg.af("funkMaskin234.func1", function(){
+var func1 = function(){
-        runAnimation({
+	runAnimation({
-            x:'3',
+ x:'3',
-            y:'6'
+ y:'6'
-        });
+	});
-    });
+};
-    mlg.af("funkMaskin234.func2", function(){
+var func2 = function(){
-        runAnimation({
+	runAnimation({
-            x:'\\text{-2}',
+ x:'\\text{-2}',
-            y:'1'
+ y:'1'
-        });
+	});
-    });
+};
-    mlg.af("funkMaskin234.func3", function(){
+var func3 = function(){
-        runAnimation({
+	runAnimation({
-            x:'7',
+ x:'7',
-            y:'10'
+ y:'10'
-        });
+	});
-    });
+};
-    mlg.af("funkMaskin234.func4", function(){
+var func4 = function(){
-        runAnimation({
+	runAnimation({
-            x:'{\\text{-9}}',
+ x:'{\\text{-9}}',
-            y:'{\\text{-6}}'
+ y:'{\\text{-6}}'
-        });
+	});
-    });
+};
-    mlg.af("funkMaskin234.func5", function(){
+var func5 = function(){
-        runAnimation({
+	runAnimation({
-            x:'0',
+ x:'0',
-            y:'3'
+ y:'3'
-        });
+	});
-    });
+};
+b.txt(3.5,-0.5,'\\text{Välj }x\\text{-värde:}');
+b.button(0.5, -1.2, 'x=\\text{-}9', func1, {mathMode:true, width:70});
+b.button(2, -1.2, 'x=\\text{-}2', func2, {mathMode:true, width:70});
+b.button(3.5, -1.2, 'x=0', func3, {mathMode:true, width:70});
+b.button(5, -1.2, 'x=3', func4, {mathMode:true, width:70});
+b.button(6.5, -1.2, 'x=7', func5, {mathMode:true, width:70});
 </jsxgpre>
-<div style="text-align:center;"><translate><!--T:3-->
-Välj ''x''-värde:</translate></div>
-<div class='jsx-btn-container'>
-<jsxbtn onclick='mlg.cf("funkMaskin234.func4")'>$x=\text{-9}$</jsxbtn>
-<jsxbtn onclick='mlg.cf("funkMaskin234.func2")'>$x=\text{-2}$</jsxbtn>
-<jsxbtn onclick='mlg.cf("funkMaskin234.func5")'>$x=0$</jsxbtn>
-<jsxbtn onclick='mlg.cf("funkMaskin234.func1")'>$x=3$</jsxbtn>
-<jsxbtn onclick='mlg.cf("funkMaskin234.func3")'>$x=7$</jsxbtn>
-</div>
 <translate><!--T:5-->
 Omvandlingsregeln här kan tolkas i ord som "addera 3". Utvärdet $y$ bildas alltså genom att addera 3 till invärdet $x.$</translate> <t1><translate><!--T:6-->

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Versionen från 13 oktober 2022 kl. 04.17

Funktion

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