An online graphing calculator to graph and determine the properties of functions. This graphing calculator accepts most mathematical functions. A quick reference list of supported functions and operations is provided below.
How to Use: Enter the expression defining function \( f(x) \) using the small letter x as the variable, then click "Plot f(x)".
Tip: Hover your mouse cursor over the graph to trace coordinates, or use the toolbar options in the top right of the graph to zoom, pan, or download the plot as a PNG file.
All functions listed below are accepted by this calculator and can be copied and pasted directly into the \( f(x) \) input window above:
| Category | Syntax & Expression | Description |
|---|---|---|
| Trigonometric | sin(x), cos(x), tan(x), cot(x), sec(x), csc(x) |
Sine, cosine, tangent, cotangent, secant, cosecant |
| Inverse Trig | asin(x), acos(x), atan(x) |
Arcsine, arccosine, arctangent |
| Hyperbolic | sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch(x) |
Hyperbolic trigonometric functions |
| Logarithmic | log(x, a), log(x) |
Logarithm to base \( a \) and natural log (base \( e \)) |
| Exponential | a^x, e^x |
Exponential functions |
| Absolute Value & Square Root | abs(x), sqrt(x) |
Absolute value and square root functions |
| Constants & Syntax | pi, e |
Special constants (leave a space or operator between constants and variables, e.g., sin(pi*x)) |
sin(pi*x)-x^2atan(2*x-2)-2exp(x^2-1)+log(x,3)Learn how to find intercepts graphically and verify algebraically:
2 x - 4 in the \( f(x) \) window to graph \( f(x) = 2x - 4 \). Find the \( x \)-intercept (solution to \( f(x) = 0 \)) and \( y \)-intercept (\( f(0) \)) graphically, and check analytically.x^2 - 2 x - 3 to graph \( f(x) = x^2 - 2x - 3 \). Determine the \( x \)- and \( y \)-intercepts graphically and verify by solving \( x^2 - 2x - 3 = 0 \) and calculating \( f(0) \).Test function symmetry using the graph and analytical definitions (\( f(x) = f(-x) \) for even, \( f(x) = -f(-x) \) for odd):
abs(x) (absolute value). Determine whether \( f \) is even, odd, or neither.x^2 + abs(x) and test symmetry.x^3 and test symmetry.x^3 + 1/x and test symmetry.x^3 + abs(x) and test symmetry.Analyze intervals visually and algebraically:
sqrt(4 - x^2). Verify graphically that the domain is \([-2, 2]\) and range is \([0, 2]\).sqrt(x^2 - 9) and determine its domain and range.-2*sin(x) and determine its domain and range.sqrt(-x + 1) and determine its domain and range.1 / (x^2 - 1) and determine its domain and range.Free printable graph paper is available.