randRangeNonZero(-3, 3) randRangeNonZero(-3, 3) randRangeNonZero(-3, 3) function(a) { return (a === 1) ? "" : (a === -1) ? "-" : a; } [SIGNIFY(A), SIGNIFY(B), SIGNIFY(C)] randFromArray([ [function(x) { return B * x + C; }, BSHOW + " x + " + C], [function(x) { return B / 2 * x * x + A * x + C; }, ((B === 2) ? "" : (B === -2) ? "-" : (B / 2)) + " x^2 + " + ASHOW + " x + " + C], [function(x) { return B * sin(C * x / Math.PI) + A; }, BSHOW + " \\sin\\left(" + CSHOW + " x / \\pi\\right) + " + A], [function(x) { return B * pow(Math.E, C * x / 3) + A; }, BSHOW + "e^{" + ((abs(C) === 3) ? SIGNIFY(C/3) + "x" : CSHOW + " x / 3") + "} + " + A] ]) (function() { var xs = chooseXValues(FUNC, 1); if (xs.length >= 5) { return sortNumbers(shuffle(xs, 5)); } else { xs = chooseXValues(FUNC, 2); return sortNumbers(shuffle(xs, 5)); } })()
0.5

Create a table of values for the function in the graph below. Use at least 5 different points. Enter the values in the table as decimals.

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function(s) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); plot(FUNC, [-10, 10], { stroke: BLUE });
Enter your data in the table below.
 x y
(function(){ var guess = []; $(".ttable tr").each(function() { var input = [];$(this).children().each(function() { input.push($(this).children().val()); }); guess.push(input); }); return guess; })() var attempted = 0; var correct = 0; var xs = []; for (var i = 0; i < 8; ++i) { if ($.trim(guess[i]) !== "" && $.trim(guess[i]) !== "") { attempted += 1; var x = parseFloat(guess[i]), y = parseFloat(guess[i]); if (abs(FUNC(x) - y) < CORRECTOFFSET) { correct += 1; xs.push(x); } } } if (attempted < 5) { return "You must enter 5 or more points"; } xs = KhanUtil.sortNumbers(xs); var different = 1; for (var i = 0; i < correct - 1; ++i) { if (xs[i + 1] - xs[i] >= 0.5) { different += 1; } } return different === attempted; You can look at function in many different ways, including a graph and a table. Here, we have a function modeled in a graph, and we want to store some information about it at a couple points by modeling it as a table. To represent it as a table, take any five points on the graph, and list them in the table. For example, we can look at the point with an x-value of EXAMPLES. The y-value at this point is round(2 * FUNC(EXAMPLES)) / 2, which we find from the graph. line([EXAMPLES, -11], [EXAMPLES, 11], { strokeWidth: 1, stroke: ORANGE }); circle([EXAMPLES, FUNC(EXAMPLES)], 0.2, { stroke: ORANGE, fill: ORANGE }); To record this in our table, put EXAMPLES in the x column, and round(2 * FUNC(EXAMPLES)) / 2 in the y column. We can do this with 4 other x-values, such as EXAMPLES, EXAMPLES, EXAMPLES, and EXAMPLES. We can find the y-values at these points by finding them on the graph as well. for (var i = 1; i < 5; ++i) { line([EXAMPLES[i], -11], [EXAMPLES[i], 11], { strokeWidth: 1, stroke: ORANGE }); circle([EXAMPLES[i], FUNC(EXAMPLES[i])], 0.2, { stroke: ORANGE, fill: ORANGE }); } From this, five points on the graph are:  (x, round(FUNC(x) * 2) / 2)  Create a graph for the function that is modeled below by plotting the points on the graph.  x y x+"\\hphantom{.0}"  roundToNearest(0.5, FUNC(x)).toFixed(1) .replace(/\.0$/, "\\hphantom{.0}") 
graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function(s) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); addMouseLayer(); graph.points = []; var drawn = false; graph.graphFunc = function() { if (!drawn) { drawn = true; var func = plot(FUNC, [-10, 10], { stroke: ORANGE, opacity: 0.0 }); func.animate({ opacity: 1.0 }, 800); } _.invoke(graph.points, "toFront"); }; graph.checkAnswer = function() { var used = [false, false, false, false, false]; _.each(EXAMPLES, function(x) { var y = roundToNearest(0.5, FUNC(x)); var done = false; _.each(graph.points, function(pt, i) { if (!done) { var coord = pt.coord; if (coord === x && coord === y) { used[i] = true; done = true; } } }); }); return _.all(used, _.identity); }; graph.moved = false; graph.checkPoints = function() { if (graph.checkAnswer()) { graph.graphFunc(); } graph.moved = true; return true; }; for (var i = 0; i < 5; ++i) { graph.points.push(addMovablePoint({ coord: [2 * i - 4, 0], snapX: 0.5, snapY: 0.5, onMoveEnd: graph.checkPoints })); }
Plot the points given in the table on the graph, then check your answer.
[ graph.moved, graph.checkAnswer(), _.pluck(graph.points, "coord") ]
if (!guess) { return ""; } else { return guess; }
_.each(graph.points, function(pt, i) { pt.setCoord(guess[i]); });

We can look at a function in many different ways, including a table and a graph. Here, we have information about a function at a few points, and we are trying to gain a more general view of the function by plotting those points in a graph.

To represent it as a graph, take all the points listed in the table, and plot them on the graph.

For example, let's look at the point  (EXAMPLES, roundToNearest(0.5, FUNC(EXAMPLES))) .

We need to move one of the points to this position to represent plotting it on the graph.

var endpt = [EXAMPLES, roundToNearest(0.5, FUNC(EXAMPLES))]; line([-4, 0], endpt, { arrows: "->" }); graph.points.moveTo(endpt, endpt); graph.points.toFront();

Now, plot the remaining four points by placing the remaining points on the given 'X's.

for (var i = 1; i < 5; ++i) { var x = EXAMPLES[i]; var y = roundToNearest(0.5, FUNC(x)); line([x - 0.5, y - 0.5], [x + 0.5, y + 0.5], { stroke: PINK }); line([x + 0.5, y - 0.5], [x - 0.5, y + 0.5], { stroke: PINK }); _.invoke(graph.points, "toFront"); }
randFromArray([ [function(x) { return B * x + C; }, BSHOW + " x + " + C], [function(x) { return B / 2 * x * x + A * x + C; }, ((B === 2) ? "" : (B === -2) ? "-" : (B / 2)) + " x^2 + " + ASHOW + " x + " + C] ]) (function() { var xs = chooseXValues(FUNC, 1); if (xs.length >= 5) { return sortNumbers(shuffle(xs, 5)); } else { xs = chooseXValues(FUNC, 2); return sortNumbers(shuffle(xs, 5)); } })() 0.01

Create a table with at least five different points in it created from the function. Enter the values in the table as decimals.

FUNCSHOW

You can look at a function in many different ways, including an equation and a table. We have an equation, and in order to see more clearly how the function acts at few points, we are going to record information about it in a table.

To represent it as a table, pick some x values to plug into the equation, and record that x and the result of plugging it into the equation in the table.

For example, try plugging in EXAMPLES to the equation.

The result of f(EXAMPLES) is roundToNearest(0.1, FUNC(EXAMPLES)). Record this in the table by putting EXAMPLES in the x column, and roundToNearest(0.1, FUNC(EXAMPLES)) in the cooresponding y column.

Now, choose four more x values to plug into the equation. Let's try the numbers EXAMPLES, EXAMPLES, EXAMPLES, and EXAMPLES.

By plugging into the equation, we get:

f(x) = roundToNearest(0.1, FUNC(x))