Tools
Graphing calculator
Online graphing calculator
Plot mathematical functions and explore their graphs with zoom and pan.
x^2sin(x)sqrt(x)log(x)abs(x)2*x + 1exp(x)tan(x)About this tool
Seeing a function drawn out helps you understand it: where it crosses the axes, where it rises, whether it has asymptotes, or how two curves compare. This graphing calculator plots several functions at once, each in its own colour, and handles inequalities too, shading the region that satisfies them. It is useful for revision, lesson planning or checking an exercise at a glance.
Type a function into the y₁ row using x as the variable, such as sin(x) or x^2 - 3. “Add function” gives you more rows. The operator button cycles through =, <, >, ≤ and ≥; the colour swatch changes the colour and the eye icon hides the plot. Drag the graph to pan and use the mouse wheel to zoom. Under View, set the X and Y range by hand or use the zoom presets, and Trace gives you the y value for any x.
The graph is drawn in your browser with the mathjs and Mafs libraries, and your functions are not sent anywhere. log means base-10 logarithm and ln the natural log. It only plots explicit functions of the form y = f(x): implicit curves such as circles, polar coordinates and 3D are not supported. On touch screens, dragging and wheel zoom are unavailable, so change the view with the range fields and presets.
How do I use the graphing calculator?
- Type the first function in the y₁ row using x as the variable, for example x^2 - 3 or sin(x).
- Click “Add function” to draw another curve on the same graph; each one gets its own colour.
- To plot an inequality, click the operator button until it shows <, >, ≤ or ≥: the region that satisfies it is shaded.
- Drag the graph to move around and use the mouse wheel to zoom. On a phone, change the view with the ranges in “View” or a preset.
- Use “Trace” to find the value of y for a given x and check a result.
Which operations and functions can I type?
Basic operations are written as on any calculator: + to add, - to subtract, * to multiply, / to divide and ^ for powers (x^3 is x cubed). Use brackets to group: (x + 1)^2 is not the same as x + 1^2.
For square roots type sqrt(x); for absolute value, abs(x); for the exponential, exp(x). The trigonometric functions sin(x), cos(x) and tan(x) work in radians, so a full period of sine is 2·pi long. The constants pi and e can be typed as they are. log(x) is the base-10 logarithm and ln(x) the natural logarithm.
If a function does not appear, the usual culprit is an unclosed bracket or an implicit multiplication that should be written with *: 2*x rather than 2x, and 3*sin(x) rather than 3sin(x).
How do you read the graph of a function?
The points where the curve crosses the x-axis are the solutions of f(x) = 0. Where it crosses the y-axis is the value of the function at x = 0. If you plot two functions, the points where they cross are the solutions of f(x) = g(x); zoom in on the crossing to read the coordinates more precisely and confirm them with “Trace”.
A curve that rises from left to right is increasing on that stretch; if it falls, it is decreasing. Peaks and valleys are local maxima and minima. When the curve shoots up or down near a value of x —like 1/x near 0— there is a vertical asymptote.
Examples to get started
To see how a parabola changes, plot x^2, x^2 + 2 and (x - 2)^2 together: the second moves up and the third shifts right. To compare growth, try x, x^2 and 2^x. For trigonometry, sin(x) and cos(x) together show the phase shift between them. And to practise inequalities, y > x^2 - 4 shades the whole region above the parabola.
Frequently asked questions
How do I plot two functions to see where they intersect?
Type the first into y₁, press “Add function” and type the second into y₂. Each gets its own colour; zoom in on the crossing and use Trace to check the values.
Can I graph inequalities such as y > x²?
Yes. Press the operator button until > appears, then type x^2. The region that satisfies the inequality is shaded; < and > draw a dashed boundary, while ≤ and ≥ draw a solid one.
Which zoom preset should I use for trig functions?
Trig sets the view from -2π to 2π horizontally and -4 to 4 vertically, which shows a couple of periods of sine, cosine or tangent.
How do I type roots, powers and absolute values?
Use sqrt(x) for square roots, ^ for powers (x^3), abs(x) for absolute value and exp(x) for e to the power x. Always multiply with *, as in 2*x.