Graph the punctured interval 0 < |x-center| < radius/10.
Show the punctured interval by dragging the left and right (white-filled) orange
dots to the endpoints of the punctured interval.
The middle dot should always stay halfway between the two outside dots.
It represents the "puncture" at the midpoint of the interval.
Don't try to move it yourself; it will automatically reposition
itself into the center of the punctured interval, as you move the outer dots.
init({
range: [[LOWER_BOUND - 1, UPPER_BOUND + 1], [-1, 1]]
});
line([LOWER_BOUND, 0], [UPPER_BOUND, 0]);
for (var x = LOWER_BOUND; x <= UPPER_BOUND; x++) {
line([x, -0.2], [x, 0.2]);
}
for (var J = LOWER_BOUND; J <= UPPER_BOUND; J++) {
label([J, -0.53], ((J - centerposition)/10) + center, "center", { color: "#6495ED" });}
addMouseLayer();
graph.movablePoint = addMovablePoint({
constraints: { constrainY: true } ,
normalStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
highlightStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
});
graph.movablePoint.onMove = function( x, y ) {
graph.movableLineSegment.coordA = graph.movablePoint.coord;
graph.movableLineSegment.transform();
xcoord = (graph.movablePoint.coord[0] + graph.movablePoint2.coord[0] ) / 2;
graph.centerPoint.setCoord([ xcoord , 0 ]);
var newx = round(x);
if (abs(newx - x) < 0.25) {
x = newx;
}
return [min(max(LOWER_BOUND, x), UPPER_BOUND), y];
};
graph.movablePoint2 = addMovablePoint({
coord: [UPPER_BOUND,0] ,
constraints: { constrainY: true } ,
normalStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
highlightStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
});
graph.movablePoint2.onMove = function( x, y ) {
graph.movableLineSegment.coordZ = graph.movablePoint2.coord;
graph.movableLineSegment.transform();
xcoord = (graph.movablePoint.coord[0] + graph.movablePoint2.coord[0] ) / 2;
graph.centerPoint.setCoord([ xcoord , 0 ]);
var newx = round(x);
if (abs(newx - x) < 0.25) {
x = newx;
}
return [min(max(LOWER_BOUND, x), UPPER_BOUND), y];
};
graph.centerPoint = addMovablePoint({
coord: [(UPPER_BOUND+LOWER_BOUND)/2,0] ,
constraints: { constrainX: true, constrainY: true } ,
normalStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
highlightStyle: {
fill: "#FFFFFF",
stroke: KhanUtil.ORANGE
},
});
graph.movableLineSegment =
addMovableLineSegment({
normalStyle: {
stroke: ORANGE,
"stroke-width": 5
},
coordA:graph.movablePoint.coord,
coordZ:graph.movablePoint2.coord,
fixed:true
});
graph.movablePoint.visibleShape.toFront();
graph.movablePoint2.visibleShape.toFront();
graph.centerPoint.visibleShape.toFront();
Move the orange dots to select your answer.
[graph.movablePoint.coord[0],graph.movablePoint2.coord[0]]
return (abs(centerposition - radius - min(guess[0],guess[1])) < 0.001)
&&
(abs(centerposition + radius - max(guess[0],guess[1])) < 0.001);
|x-center| is the distance from x
to center.
So we need to graph all numbers x such that
the distance from x to center
is both (greater than 0) and (less than radius/10).
This would be the punctured open interval centered at center
with radius radius/10.
In other words, the punctured open interval from center - radius/10
to center + radius/10.
In other words, the punctured open interval from center - (radius/10)
to center + (radius/10).
graph.movablePoint.moveTo(LOWER_BOUND, 0);
graph.movablePoint2.moveTo(UPPER_BOUND, 0);
style({ stroke: "#6495ED", fill: "#6495ED", strokeWidth: 2.5, arrows: "->" });
line([LOWER_BOUND, 0], [centerposition - radius, 0]);
graph.movablePoint.visibleShape.toFront();
style({ stroke: "#6495ED", fill: "#6495ED", strokeWidth: 2.5, arrows: "->" });
line([UPPER_BOUND, 0], [centerposition + radius, 0]);
graph.movablePoint2.visibleShape.toFront();
Now follow the blue arrows above. That is, drag
the left (white-filled) orange dot over to center - (radius/10)
and drag
the right (white-filled) orange dot over to center + (radius/10).
I can drag the dots for you -- just ask for the next hint.
graph.movablePoint.moveTo(centerposition - radius, 0);
graph.movablePoint2.moveTo(centerposition + radius, 0);
I've dragged the dots into their proper position.
Now click on "Check Answer" or "Try Again".