Graphing Calculator
Plot up to 6 functions simultaneously. Supports polynomials, trig, exponentials, logarithms, and more. Scroll to zoom, drag to pan.
A graphing calculator plots mathematical functions as curves on an x–y coordinate plane. Enter any function of x — such as sin(x), x²−4, or 2x+1 — and the calculator draws the curve instantly. Use it to visualize shapes, find x-intercepts (zeros), identify maxima and minima, and compare how different functions relate to each other.
Scroll to zoom · Drag to pan · Up to 6 simultaneous functions · Click color dot to toggle
How to Use This Graphing Calculator
- 1Enter a function
Type any function of x in the input box: sin(x), x^2+2x-3, 2*x+1, ln(x), |x|, or e^x. Implicit multiplication works — you can write 2x instead of 2*x, and 3sin(x) instead of 3*sin(x). Use ^ for exponents: x^3 means x³.
- 2Click + Graph (or press Enter)
The curve appears immediately in a unique color. The default view shows x from −10 to 10. If the curve is not visible, the function may be zero or undefined in this range — try zooming out.
- 3Pan and zoom to explore
Scroll your mouse wheel over the graph to zoom in or out around the cursor position. Click and drag to pan in any direction. The + and − buttons in the top-right corner also zoom. Click ⌂ to reset to the default view.
- 4Add more functions to compare
Add up to 6 functions to compare on the same graph. Each gets a distinct color (blue, red, green, amber, violet, orange). Click the color dot next to any function to toggle its visibility. Click × to remove it entirely.
Types of Functions You Can Graph
The graphing calculator supports the full range of functions taught in secondary school and university mathematics. Functions can be entered in natural mathematical notation — no special formatting required.
| Type | Examples to enter | What you'll see |
|---|---|---|
| Linear | 2x+1, -x+3, 0.5x | A straight line with slope and y-intercept |
| Quadratic | x^2, x^2-4, (x-2)^2+1 | U-shaped parabola (opens up or down) |
| Polynomial | x^3-3x, x^4-4x^2+3 | S-curves, W-shapes with multiple turning points |
| Trigonometric | sin(x), cos(x), tan(x) | Wave patterns; tan has vertical asymptotes |
| Exponential | exp(x), 2^x, 0.5^x | Rapid growth or decay curves |
| Logarithmic | ln(x), log(x) | Slow-growing curve; undefined for x ≤ 0 |
| Absolute value | abs(x), |x|, |x-2| | V-shape, always ≥ 0 |
| Square root | sqrt(x) | Right-facing curve; undefined for x < 0 |
| Rational | 1/x, 1/(x^2+1) | Hyperbolas; asymptotes where denominator = 0 |
| Combined | sin(x)*exp(-0.1*x) | Damped oscillation — key in engineering |
Graphing Calculators Around the World
Whether and which graphing calculator students use varies dramatically by country and curriculum. This free online tool works for everyone — but understanding your local exam rules matters.
🇺🇸 United States
The TI-84 Plus CE is the de facto standard — used in roughly 80% of US high schools. The College Board allows most graphing calculators on the SAT and all AP exams (including AP Calculus AB/BC and AP Statistics). The TI-89 Titanium is NOT allowed on SAT because its CAS (Computer Algebra System) can solve algebra symbolically. Many state assessments like the ACT allow graphing calculators. The TI-Nspire CX (non-CAS) is also popular at the AP level.
🇬🇧 United Kingdom
Graphing calculators are generally not permitted in GCSE or most A-Level mathematics examinations. The standard allowed device is the Casio fx-991EX ClassWiz — a powerful scientific calculator with no graphing capability. A-Level Further Mathematics and some MEI specifications permit the Casio fx-CG50 or similar. The focus in UK exams is on algebraic manipulation and proof, so the exam system is designed to work without a graphing display.
🌍 IB (International Baccalaureate)
The IB requires a GDC (Graphic Display Calculator) for Mathematics: Analysis and Approaches (SL and HL) and Mathematics: Applications and Interpretations. The Casio fx-CG50 and TI-84 Plus CE are both approved. The IB exam is explicitly designed with GDC questions — candidates without one are at a significant disadvantage. Students in Mathematics: Applications courses are expected to use graphical technology to explore real-world modelling.
🇦🇺 Australia
Australia permits CAS (Computer Algebra System) calculators in most state senior mathematics exams — more permissive than almost any other country. The TI-Nspire CX CAS and Casio ClassPad 400 are the standard choices in Victoria (VCE), Western Australia (WACE), and South Australia (SACE). Queensland uses the TI-Nspire (non-CAS) for its QCAA exams. The ACT (Australian Capital Territory) allows graphing but not CAS.
🇯🇵 Japan
Japan's CSAT (Center for University Admissions Examination / 共通テスト) does NOT allow calculators of any kind in the mathematics sections. Students use mental arithmetic and written methods. However, graphing calculators such as the Casio fx-CG50 are used in some secondary school instruction for visualization. The gap between Japan's rigorous manual calculation culture and the GDC-heavy IB curriculum is one of the most striking differences in global math education.
🇩🇪 Germany
Germany's Abitur calculator policy is set by each of the 16 Bundesländer separately. Bayern (Bavaria) and some others require the TI-Nspire CX CAS for the mathematics Abitur — making it one of the most technologically advanced exam environments in Europe. By contrast, Nordrhein-Westfalen (NRW) prohibits symbolic calculators. Brandenburg and others still allow only scientific (non-graphing) calculators. A student moving between German states may need a completely different calculator.
🇫🇷 France
France has allowed graphing calculators in the Baccalauréat (série générale) mathematics exam since the early 1990s. The Casio Graph 90+E and TI-83 Premium CE are popular choices. CAS calculators are generally permitted. France is notable for integrating graphical exploration into the curriculum through the digital tool Geogebra, which is freely available and widely used in classrooms alongside hardware calculators.
How to Read a Graph
Understanding what you're looking at is just as important as drawing the curve. Here are the key features to identify on any function graph:
Points where the graph crosses or touches the x-axis (y = 0). For a quadratic like x²−4, the zeros are x = 2 and x = −2. These represent solutions to the equation f(x) = 0.
Where the graph crosses the y-axis (x = 0). For f(x) = 2x+3, the y-intercept is (0, 3). There is always at most one y-intercept for a function.
For linear functions, slope is the steepness — rise over run. In y = 2x+1, the slope is 2. A positive slope goes up left-to-right; negative goes down. Steeper = larger absolute slope.
The lowest or highest point on a curved graph. For y = x², the vertex is at (0, 0). For y = −(x−2)²+5, the maximum (vertex) is at (2, 5). This is where the function changes from increasing to decreasing or vice versa.
Trig functions repeat in cycles. sin(x) has period 2π (≈6.28) and amplitude 1. sin(2x) has period π — it completes twice as many cycles. 3sin(x) has amplitude 3 — the peaks reach y=3.
Lines the graph approaches but never reaches. tan(x) has vertical asymptotes at x = π/2, 3π/2… because tan is undefined there. 1/x has both a vertical asymptote at x=0 and a horizontal asymptote at y=0.
Graphing vs Scientific Calculator
A scientific calculator evaluates a single numerical expression: type sin(30) and get 0.5.
It gives you a number.
A graphing calculator evaluates the function across thousands of x values and draws the resulting curve — it gives you a picture.
The picture reveals zeros, maxima, minima, asymptotes, and the overall behaviour of the function at a glance.
Both tools are complementary. Use the scientific calculator to verify specific values (sin(π/6) = 0.5), and use the graphing calculator to understand the full shape of a function before solving it analytically. For pure number crunching — percentages, taxes, unit conversions — a scientific calculator or specialized tool is faster.