Function Grapher
Plot one or more y=f(x) with intercepts and key points
About this calculator
The Function Grapher plots one or more functions y = f(x) over a chosen viewing window and analyzes each curve: the y-intercept f(0), every x-intercept found by a sign-change scan of 1200 samples, and the local maxima and minima located as roots of the numeric derivative and classified by the second derivative. Expressions are parsed by a shared math core supporting sin, cos, exp, ln, powers, and more; unparseable functions and invalid windows are reported clearly. Useful for precalculus, calculus, and quick visual checks.
How to use the Function Grapher calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- x² − 4 on [−5, 5] → x-intercepts −2 and 2, y-intercept −4, minimum at (0, −4)
- x³ − 3x → roots −1.732…, 0, 1.732…; local max (−1, 2) and min (1, −2)
- sin(x) on [−7, 7] → zeros at 0 and ±3.141592654, extrema ±1 at ±1.570796327
- Graph x² − 4 and x³ − 3x together to compare their intercepts in one window
Frequently asked questions
How does the Function Grapher calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Function Grapher calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.