Graphing Calculator
Graphing Calculator works out Function plotted and Value at the query point from Plot type, Function and Second function (optional). The default figures on this page give function plotted of x^2 - 4; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- f(x) = x^2 - 4
- Sampled 21 points on [-10, 10] at x_i = -10 + 20 * i / 20.
- Sampled range: -4 to 96 over 21 of 21 points.
- Zeros in the interval: -2, 2 (exact grid zeros plus bisected sign changes).
Zeros in the intervaltable
Sampled pointstable
| x | y |
|---|---|
| -10 | 96 |
| -9 | 77 |
| -8 | 60 |
| -7 | 45 |
| -6 | 32 |
| -5 | 21 |
| -4 | 12 |
| -3 | 5 |
| -2 | 0 |
| -1 | -3 |
| 0 | -4 |
| 1 | -3 |
| 2 | 0 |
| 3 | 5 |
| 4 | 12 |
| 5 | 21 |
| 6 | 32 |
| 7 | 45 |
| 8 | 60 |
| 9 | 77 |
| 10 | 96 |
Its 6 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the Graphing Calculator calculates
Plots y = f(x), a piecewise function or a z = f(x, y) surface over a chosen domain, returning the sampled points, the range, the intercepts, the zeros and any intersection with a second curve.
How to use this Graphing Calculator
Enter Plot type, Function, Second function (optional) and Variable. Function plotted updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Function plotted, Value at the query point and Smallest sampled value.
The method follows OpenStax College Algebra 2e, section 3.2 Domain and Range, OpenStax College Algebra 2e, section 3.4 Composition of Functions / piecewise definitions, Burden & Faires, Numerical Analysis, section 2.1 (the Bisection Method) and W3C Scalable Vector Graphics (SVG) 1.1, section 8.3 Path data.
y = x^2 - 4 on [-3, 3] example
With Function: x^2 - 4, x from: -3, x to: 3, Sample points: 13, the calculator returns Zeros in the interval: see result table, y-intercept: -4, Smallest sampled value: -4. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Function plotted, Value at the query point and Smallest sampled value. The inputs you can vary are Plot type, Function, Second function (optional), Variable, x from and x to.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
Why are graphing calculators banned?
Plots y = f(x), a piecewise function or a z = f(x, y) surface over a chosen domain, returning the sampled points, the range, the intercepts, the zeros and any intersection with a second curve. On the figures this page opens with — x from -3, x to 3 and evaluate at x 1 — the function plotted is x² - 4. Put your own figures in their place and the working updates beside the result.
Are graphing calculators still worth it?
It needs Plot type, Function, Second function (optional), Variable, x from and x to. Nothing else is required, and the figures stay in your browser.
What information do I need for the Graphing Calculator?
You need Plot type, Function, Second function (optional), Variable, x from, x to, y from (3D) and y to (3D). The page opens with default figures that give function plotted of x^2 - 4, so you can see the scale before entering your own.
What does this Graphing Calculator show?
It shows Function plotted, Value at the query point, Smallest sampled value, Largest sampled value, y-intercept, Zeros in the interval, Intersections with the second curve and Sampled points, with the working and any warnings for your entries.
Can I check how the Graphing Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.