MENUFunction Graph Plotter and Analyzer
Type a function and its graph appears at once: functions, polar and parametric curves, points and inequalities, with sliders for parameters, roots and intersections. Drag to move the graph, zoom with the wheel or two fingers, and copy the link to share exactly what is on your screen. It also draws equations such as x2 + y2 = 25, derivatives, tangents and areas, and studies a function for you: domain, extrema, asymptotes and the variation table.
How to type
Type one expression per row. The tool recognises what you typed and shows it under the row as a formula, so you can check how it was read.
| You type | It means | Notes |
|---|---|---|
2.5, .5, 1e-3 | numbers | Use a dot for decimals: 2.5, not 2,5. |
+ - * / ^ | operations | ^ is a power: x^2. 2^3^2 = 29 = 512 and -x^2 = −(x2). |
2x, 3(x+1), (x+1)(x-1) | multiplication without a sign | 1/2x means ½·x. Write 1/(2x) for 1 over 2x. |
sqrt(x), √x, cbrt(x), root(n, x) | roots | x^(1/3) gives the real cube root, also for negative x. |
abs(x), |x| | absolute value | |x-|x|| works too. |
sin cos tan cot | trigonometric functions | In radians; switch to degrees in Settings. tg, ctg and sen work too. |
arcsin arccos arctan | inverse trigonometric functions | Also asin, arctg and sin^-1(x). |
ln(x), log(x), log_2(x) | logarithms | log and lg are base 10; log_b(x) and log(b, x) are base b. |
e^x, exp(x), pi, π | the numbers e and π | |
floor ceil round sign min max mod, n! | other functions | mod(a, b) has the sign of b. |
sin x, sin 2x, sin^2 x | functions without brackets | The function takes the product after it: sin 2x + 1 = sin(2x) + 1 and sin2x = (sin x)2. |
x^2, y = 2x + 1 | a function y = f(x) | “y =” can be left out. |
f(x) = x^2 - 4 | a named function | Other rows can use it: g(x) = f(x - 2) + 1. |
a = 2 | a slider | Any letter except x, y, t, e and r. A row that uses an unknown letter offers an “Add slider” button. |
x = 3 | a vertical line | |
y > x^2, x <= 1 | an inequality | The region is shaded; the border is dashed for < and >. Several inequalities show the solution of a system. |
r = 1 + cos(θ) | a polar curve | θ goes from 0 to 2π; type theta if you have no θ key. |
(cos(t), sin(t)) | a parametric curve | t goes from 0 to 2π; change the range under the row. |
(1, 2), (3, 4) | points | The row menu joins them with lines or shows their coordinates. |
x^2 {x > 0} | a domain restriction | The curve is drawn only where the condition holds: {-1 <= x <= 2}. |
x^2 + y^2 = 25, xy = 1 | an equation in x and y | The curve is drawn wherever both sides are equal. |
f'(x), f''(x) | the derivatives of a named function f | Or choose “Show derivative” in the row menu ⋯, which also names the row f(x) = …. |
tangent(f, 1), normal(f, 1) | the tangent and the normal at x = 1 | tangent(f, (0, -1)) draws every tangent through the point (0, −1). Instead of f you can type a formula: tangent(x^2, 1). Tap a point of a curve for the Tangent and Normal buttons. |
secant(f, 1, 3) | the secant through x = 1 and x = 3 | With a slider, secant(f, 1, 1+h) turns into the tangent as h gets small. |
integral(f, 0, 2) | the definite integral from 0 to 2 | The region is shaded and the parts below the x-axis are hatched; the label gives the integral and the area. |
area(f, g), area(f, g, 0, 2) | the area between two curves | Without bounds, between their first and last intersection. |
riemann(f, 0, 2, 8, left) | a Riemann sum with 8 rectangles | The last word is left, right, mid (the default) or trap (trapezoids). With a slider for n you see the sum approach the integral. |
inverse(f) | the graph of the inverse function | The mirror image of f in the line y = x. |
Tips
- Move and zoom: drag the graph, use the mouse wheel or pinch with two fingers. Double-click or double-tap zooms in; the house button goes back to the starting view.
- Key points: grey dots mark the roots, maximums, minimums and intersections of the selected curve. Point at a dot to see its coordinates (with the exact value, like x = √2, when there is one); click it, or tap it twice on a phone, to keep the label.
- Trace: move the mouse along a curve, or press and hold on a phone, to read the coordinates of any point.
- Sliders: drag a slider or press ▶ to see how the graph changes with the parameter.
- Share and save: the address bar always holds the current graph. The link button copies it; the download button saves a PNG picture or an SVG drawing for worksheets.
- Study a function: under the tool every function gets its own analysis, the one you drew last on top: domain, parity, zeros, sign, monotonicity, extrema, range, asymptotes, the variation table, which you can copy as LaTeX, and a table of values.
Examples
Each link opens the plotter with a ready graph.
- Parabola with sliders: y = a(x − h)2 + k
- Straight line y = kx + b
- Sine and cosine waves
- Unit circle with points
- Rose curve r = 2 sin 3θ
- System of inequalities y > x2 − 4, y < x + 2
- Points joined by lines
- Absolute value y = |x| and y = |x − 2| − 3
- Exponential and logarithm: y = ex, y = ln x
- Tangent and its asymptotes
- Variation table of y = x3 − 3x
- Vertical and oblique asymptote: y = (x2 + 1)/(x − 1)
- Tangent sliding along a parabola
- Secant turning into a tangent
- Area between y = x2 and y = x + 2
- Riemann sum with a slider for n
Read the Graph of a Function