$Function Grapher$

Function Grapher

Online function grapher: up to three functions on one plot, zeros, intersection points and a table of values. Polynomials, fractions, roots, absolute value, logarithms, sine and tangent.

Functions (up to three):

y =

Plot range:

x from to y from to

Examples: x^2 − 3x + 2, 1/x, sqrt(x), |x − 1|, sin(2x), 2^x, ln(x), e^(−x^2). The multiplication sign can be omitted: 2x, 3sin x.

Test yourself

The online graphing calculator plots up to three functions at once on a chosen interval, marks the zeros, the y-intercepts and the intersection points of the graphs, and gives a table of values. It supports polynomials, fractions, roots, absolute value, powers, logarithms and trigonometric functions — with breaks and asymptotes, like for 1/x and tan x.

How to enter functions

Input	Meaning
x^2, x^3, x^(1/3)	power
2x, 3(x − 1), x sin x	multiplication (the * sign can be omitted)
1/x, (x + 1)/(x − 2)	division, fraction
sqrt(x), √x, cbrt(x)	square and cube root
\|x\|, abs(x)	absolute value
sin x, cos x, tan x, cot x	trigonometric functions (argument in radians)
arcsin x, arccos x, arctan x	inverse trigonometric functions
ln x, log x, 2^x, e^x, exp(x)	logarithms (log is base 10) and exponential functions
pi, π, e	the constants π ≈ 3.14159 and e ≈ 2.71828

A function argument without brackets continues up to the next sign: sin 2x = sin(2x), while sin x · cos x is a product. When in doubt, use brackets.

Graphs of the basic functions

Linear y = kx + b — a straight line; k is the slope, b is the y-intercept.
Quadratic y = ax² + bx + c — a parabola with the vertex at x = −b / (2a); it opens upward when a > 0.
Inverse proportion y = k/x — a hyperbola with the asymptotes x = 0 and y = 0.
Square root y = √x — half of a parabola, defined for x ≥ 0.
Exponential y = a^x and logarithmic y = log_a x — the graphs are symmetric about the line y = x.
Sine wave y = sin x repeats with period 2π, y = tan x — with period π and asymptotes x = π/2 + πk.

How intersection points are found

The zeros of a function are the solutions of f(x) = 0, the intersection points of two graphs are the solutions of f(x) = g(x). The calculator finds them numerically with an accuracy of 10⁻⁹ and shows an exact number when the root is an integer, a simple fraction or a multiple of π.

Example. y = x² − 3x + 2 crosses the x-axis at x = 1 and x = 2, and the y-axis at (0, 2).

Graph transformations

Function	How to get it from the graph of y = f(x)
y = f(x) + b	shift up by b (down if b < 0)
y = f(x − a)	shift right by a (left if a < 0)
y = k · f(x)	vertical stretch by a factor of k
y = −f(x)	reflection in the x-axis
y = f(−x)	reflection in the y-axis
y = \|f(x)\|	the part below the x-axis is reflected upward