{% extends "multiple_choice_template.html" %}
{% block maincode %}
<script language=Javascript1.2><!--
Exercise.fAddNoneOfThese = false;
var curExp;

var oddMakers = new Array();
var evenMakers = new Array();
var neitherMakers = new Array();

var a;

var fofa;
var fofna;

function get_coefficient(offset) {
    var lcoef = KhanAcademy.random() * 3.5;
    if (offset)
        lcoef += Math.abs(offset);
    if (getRandomIntRange(0,1) == 0)
        lcoef *= -1;
    return lcoef;
}

oddMakers[0] = function() {
    // odd-order polynomial
    var lcoef = get_coefficient() / 2;
    var xcoef = getRandomIntRange(-3,3);
    
    a = getRandomIntRange(1,2);
    fofa = lcoef * Math.pow(a, 3) + xcoef * a;
    return 'y=' + lcoef + 'x^3+' + xcoef + 'x';
}

oddMakers[1] = function() {
    // diagonal line
    var lcoef = get_coefficient() / 2;
    
    a = getRandomIntRange(1, 5);
    fofa = lcoef * a;
    return 'y=' + lcoef + 'x';
}

oddMakers[2] = function() {
    // sin x + ax 
    var lcoef = get_coefficient();
    var xcoef = getRandomIntRange(-2,2);
    
    a = getRandomIntRange(1, 3);
    fofa = lcoef * Math.sin(a) + xcoef * a;
    return 'y=' + lcoef + 'sin(x)+' + xcoef + 'x';
}

evenMakers[0] = function() {
    // horizontal line
    var cons = get_coefficient(0.5);

    a = getRandomIntRange(1, 5);
    fofa = cons;
    return 'y=' + cons;
}

evenMakers[1] = function() {
    // acos x
    var lcoef = get_coefficient(0.25);
    
    a = getRandomIntRange(1, 4);
    fofa = lcoef * Math.cos(a);
    return 'y=' + lcoef + 'cos(x)';
}

evenMakers[2] = function() {
    // abs(x)
    var lcoef = get_coefficient(0.25) / 2;
    var cons = get_coefficient();
    
    a = getRandomIntRange(1, 3);
    fofa = lcoef * Math.abs(a) + cons;
    return 'y=' + lcoef + 'abs(x)+' + cons;
}

evenMakers[3] = function() {
    // even-order polynomial
    var lcoef = get_coefficient(0.01);
    var cons = getRandomIntRange(-5,5);
    
    a = getRandomIntRange(1,3);
    fofa = lcoef * Math.pow(a, 2) + cons;
    return 'y=' + lcoef + 'x^2+' + cons;
}

neitherMakers[0] = function() {
    // shifted parabola
    var lcoef = get_coefficient(0.5);
    var xcoef = get_coefficient(1);
    
    a = 1;
    fofa = lcoef * Math.pow(a, 2) + xcoef * a;
    
    fofna = lcoef * Math.pow(a, 2) + xcoef * a * -1;
    return 'y=' + lcoef + 'x^2+' + xcoef + 'x';
}

neitherMakers[1] = function() {
    // shifted odd-order polynomial
    var ocoef = get_coefficient(0.01);
    var icons = get_coefficient(1);
    var xcoef = getRandomIntRange(-1,1);
    var ocons = getRandomIntRange(-3,3)
    
    a = getRandomIntRange(1,3);
    fofa = ocoef * Math.pow(a + icons, 3) + xcoef * a + ocons;
    
    fofna = ocoef * Math.pow(-1 * a + icons, 3) + xcoef * a * -1 + ocons;
    return 'y=' + ocoef + '(x+' + icons + ')^3+' + xcoef + 'x+' + ocons;
}

neitherMakers[2] = function() {
    // shifted even-order polynomial

    var ocoef = get_coefficient(0.1);
    var icons = get_coefficient(0.75);
    var ocons = getRandomIntRange(-3,3);
    
    a = 1;
    fofa = ocoef * Math.pow(a + icons, 2) + ocons;
    
    fofna = ocoef * Math.pow(-1 * a + icons, 2) + ocons;
    return 'y=' + ocoef + '(x+' + icons + ')^2+' + ocons;
}

var funcCategory = getRandomIntRange(0, 2);
switch(funcCategory) {
    case 0:
        curExp = oddMakers[getRandomIntRange(0, oddMakers.length - 1)]();
        setCorrectAnswer('`Odd`');
        fofna = -1 * fofa;
        
        addWrongChoice('`Neither`');
        addWrongChoice('`Even`');
        break;
    case 1:
        curExp = evenMakers[getRandomIntRange(0, evenMakers.length - 1)]();
        setCorrectAnswer('`Even`');
        fofna = fofa;
        
        addWrongChoice('`Neither`');
        addWrongChoice('`Odd`');
        break;
    case 2:
        curExp = neitherMakers[getRandomIntRange(0, neitherMakers.length - 1)]();
        setCorrectAnswer('`Neither`');
        
        addWrongChoice('`Even`');
        addWrongChoice('`Odd`');
}

function graph_update() {

	present.setBorder(0);
	
	present.initPicture(-8,8, -8, 8);
	present.marker="arrow";
	present.line([0,0], [-8, 0]);
	present.line([0,0], [8, 0]);
	present.line([0,0],[0,-8]);
	present.line([0,0],[0,8]);
	
	present.strokewidth = 1.5;
	present.stroke = "blue";
	//alert(curExp);
	present.plot(curExp);
}


function draw_next_step()
{
	present.fontstyle = "normal";
	present.fontfamily = "sans-serif";
	present.fontsize = "16";


	if (Exercise.steps_given==0)
	{
	    //alert('fofa = ' + fofa + ', a = ' + a);
	    //alert(curExp);
		present.strokedasharray="2,2";
		present.fontfill="black";
		present.marker="none";
		
		present.stroke= "red";
		present.line([a, 0], [a, fofa]);
		present.text([a, 0], "a", below);
		
		present.line([0, fofa], [a, fofa]);
		present.text([0, fofa], "f(a)", left);	
	}
	else if (Exercise.steps_given==1)
	{
		present.stroke= "green";
	    present.line([-1 * a, 0], [-1 * a, fofna]);
		present.text([-1 * a, 0], "-a", below);
		
		present.line([0, fofna], [-1 * a, fofna]);
		present.text([0, fofna], "f(-a)", right);
	}
	else if (Exercise.steps_given==2)
	{
        document.getElementById('hint'+funcCategory).style.display = 'block';
	}
	Exercise.steps_given++;
}


//-->
</script>
{% endblock maincode %}

{% block maincell %}

<script language=Javascript1.2><!--

writeText('<span style="color:blue">`f(x)`</span> is graphed below. Is <span style="color:blue">`f(x)`</span> even, odd, or neither?');

//-->
</script>
<br>

<table><tr>
    <td style="width:550px">
        <iframe name="present" frameborder=0 src="/graphpage.html?w=500&h=400" height="430" width="100%"></iframe>
    </td><td>
        <div id="hint0" style="font-family:sans-serif;font-size:16;display:none;">
        `f(a)=-f(-a)`,<br/>so the function is odd.<br/>
        Notice that the graph looks "flipped" across the origin.</div>
        <div id="hint1" style="font-family:sans-serif;font-size:16;display:none;">
        `f(a)=f(-a)`,<br/>so the function is even.<br/>
        You can see that the graph is symmetric around the vertical axis.</div>
        <div id="hint2" style="font-family:sans-serif;font-size:16;display:none;">
        `f(a)!=f(-a)`, and `f(a)!=-f(-a)`,<br/>
        so the function is neither odd nor even.<br/>
        Also, the graph isn't symmetric around the vertical axis (even),
        and it doesn't "flip" over the origin (odd).</div>
    </td>
</tr></table>
{% endblock maincell %}

{% block hintfunction %}draw_next_step(){% endblock hintfunction %}