Graphing calculator
Plot up to three real-valued functions safely, generate a value table, and estimate visible x-intercepts and y-intercepts. Expressions are parsed locally without executing typed code.
Supported graphing syntax
| Type | Accepted syntax | Example |
|---|---|---|
| Operators | + − * / ^ and parentheses | (x+2)^2/4 |
| Implicit multiplication | Number, variable or parenthesis placed together | 2x, 3(x-1) |
| Constants | pi and e | sin(pi*x) |
| Trigonometry | sin, cos, tan, asin, acos, atan | cos(x) |
| Other functions | sqrt, abs, ln, log, exp, floor, ceil, round | sqrt(abs(x)) |
Angles use radians. log is base 10 and ln is the natural logarithm. Exponentiation is right-associative, so 2^3^2 means 2(3²). Unary minus follows normal mathematical precedence: -x^2 means −(x²).
How the graph and roots are calculated
The calculator tokenizes each expression, builds a mathematical syntax tree, and evaluates that tree across the selected x-range. It does not call JavaScript eval. Curves are sampled across the canvas and discontinuities are left unconnected when the calculated jump is too large.
Visible roots are approximated by scanning the selected interval for sign changes and then applying bisection. A candidate is retained only when substituting it back into the function gives a value close to zero. Even-multiplicity roots that merely touch the x-axis can be missed unless a sample lands very close to them.
Checked examples
| Expression | Expected feature |
|---|---|
| x^2-4 | Visible roots at x = −2 and x = 2 |
| sin(x) | Root at x = 0 and repeating roots separated by π |
| 2x+3 | y-intercept 3 and x-intercept −1.5 |
| 1/x | Undefined at x = 0; the asymptote is not a root |
| sqrt(x) | Undefined for negative x in the real-number graph |
| exp(x) | y-intercept 1 and no real x-intercept |
Frequently asked questions
Can I enter more than one function?
Yes. Enter up to three functions. Leave an optional function blank to omit its curve and table column.
Does the calculator solve equations symbolically?
No. It estimates visible real roots numerically within the selected x-range. It does not return exact radicals, complex roots or algebraic steps.
Why is part of a curve missing?
The expression may be undefined there, outside the selected y-range, or separated by a discontinuity. Adjust the viewing window and verify the function domain.
Can I use degrees?
Trigonometric functions use radians. Convert degrees to radians inside the expression, for example sin(x*pi/180).
Related tools: Quadratic Formula Calculator, Polynomial Calculator and System of Equations Calculator.