Graphing calculator

What you can type

• Functions: y = x^2 - 3x, sin2x, e^-x, |x - 1|, sqrt(x), ln x, log_2(x)
• Your own functions: f(x) = x^3 - 3x, then f(x - 2) + 3 or f'(x)
• Sliders: any letter you have not defined, like a in y = a(x - h)^2 + k, offers a slider; ▶ animates it
• Points and lists: (2, 3), n = [1...10], (n, 2n + 1). Drag a point like (h, k) to move its sliders; a label such as (${h}, ${k}) shows its values
• Piecewise and restrictions: {x < 0: -x, x^2}, y = sqrt(x) {0 <= x <= 4}
• Calculator: int_0^2 x^2 dx, sum_(n=1)^(10) n^2, mean(y_1), nCr(5, 2)
• Started in Desmos? Import from Desmos brings in copied expressions, sliders and table cells, and tells you anything it couldn't bring in.

Regression for your IA

Paste two columns from a spreadsheet into an expression line to make a table with lists x_1 and y_1, then type a model with ~:

• y_1 ~ m x_1 + b (shows r and R²)
• y_1 ~ a x_1^2 + b x_1 + c, y_1 ~ a ln(x_1) + b, y_1 ~ a/x_1 + b
• y_1 ~ a sin(b x_1 + c) + d, y_1 ~ a e^(k x_1) + c, y_1 ~ a x_1^n, y_1 ~ L/(1 + C e^(-k x_1))

+ Image puts a photo behind the axes (or drop or paste one on the graph): drag it into place and resize it from a corner, read points off the curve into a table, then fit a model with ~. Examples has one to try.

Under every fit, What this model means explains each parameter in your context (from the axis labels in Settings), how to read R² and r, whether the residuals show a pattern, and where the model can be trusted, with questions to ask yourself. It also shows what rounding the parameters does to R², with notes on accuracy and questions for evaluating your model. It explains; the write-up stays yours. Compare models under a table fits the standard models to the same data and can test each one on points you did not use, and residual plot draws the residuals in a small second graph. Log scales in Settings straighten power and exponential data. + Note adds words to your graph.

The parameters are found by least squares, with no starting values needed. Plot the residuals with (x_1, e_1). Log mode fits the logarithms, like a GDC's exponential and power regression. For the maths behind it, see IA modelling, step by step.

Reading the graph

• Tap a curve to select it: grey dots mark its roots, turning points, y-intercept and intersections with other curves. Tap a dot for its coordinates, or drag along the curve to trace it.
• Drag to move; pinch, scroll or use + and − to zoom; ⌂ resets, ⤢ fits your data, □ makes the axes square.
• Keyboard: focus the graph, then arrow keys move and + / − zoom. Data table lists the values and points of interest.
• Share link puts the whole graph in the link (nothing is uploaded, so pictures you add are not included); Export downloads a PNG or an SVG, with your residual plots if you want them. Your graph, with its pictures, is also kept in this browser.
• On a phone, Keypad gives you ^, √, π, θ, x₁ and ~ without switching keyboards. Select a curve and tap table of values for a table.
• Save keeps it in My graphs with a free account (up to 200 graphs, and up to 5 pictures per graph), to open, rename or delete on any device.
• Pictures are made smaller in your browser before they are used (at most 1600 pixels across), which also removes the photo's hidden details such as its location.

Practising for a calculator paper? See the calculator skills guides. This grapher is our own tool; the ~ syntax follows the convention many graphing tools use.

Guides

• Regression with R² and residuals · curve fitting · residual plots
• Exponential, logarithmic and sinusoidal regression · log–log plots
• Transformations with sliders · tables of values · intersections and turning points
• Graphs of common functions, each with its key features
• How the Grapher compares with Desmos

Short address: graph.mathrevision.co.uk. Export → Embed on a website puts an interactive copy of your graph on a blog or VLE page.