# Function & Equation Grapher | Implicit Function Grapher

This powerful online function and equation grapher can graph functions f(x) and equations of the form f(x,y) = g(x,y), where each side can contain both the variables x and y, including implicitly defined functions.

An equation grapher is a more versatile tool than a function grapher, as it can graph any equation of the form g(x,y) = f(x,y), where each side of the equation can contain both x and y.

A function grapher, on the other hand, can only graph equations in the form y = f(x), where the right-hand side is an expression in x only. To graph a function, you simply need to type the right-hand side of the equation into an expression box.

To graph an equation, enter both sides of the equation, separated by an equal sign. This allows you to graph equations such as the equation of a line in point-slope form, the equation of a conic section (circles, parabolas, hyperbolas, and ellipses), level curves, and implicitly defined functions. Instructions

Tips - As you type:
• ..t is replaced by `θ`. (You can also use `x` or `t`; they are internally replaced by `θ`).
• pi is replaced by `π`.
• inf (infinity) is replaced by `∞`.
More tips
x y
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Label Axes

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Functions

Lines

1 x+1 2x

Semi-circles

√(9-x^2) -√(9-x^2)

Semi-ellipses

√(9-x^2/3) √(9-x^2/3)

Parabolas

x^2 0.5x^2-4x+1 -(0.5x^2-4x+1)

Semi-hyperbolas

√(x^2-4) -√(x^2-4)

Other graphs

√(4sin(2x)) √(4cos(2x))
Functions – Polar

Lines

2csc(θ) 2sec(θ) 1/(sin(θ) - cos(θ))

Circles

1 2 6sin(θ) 8cos(θ)

Spirals

θ θ/5 dom=(0, 10π) √(θ) dom=(0, 10π) 1/θ dom=(0, 10π)

Roses

4sin(3θ) 4sin(2θ) 4sin(5θ) 4sin(4θ)

Ellipses

1/(1-.8cos(θ)) 1/(1-.8sin(θ)) 1/(1+.8cos(θ)) 1/(1+.8sin(θ))

Parabolas

1/(1-sin(θ)) 1/(1+cos(θ)) 1/(1+sin(θ)) 1/(1-cos(θ))

Hyperbolas

1/(1+2cos(θ)) 4/(1+2sin(θ)) 1/(1-2cos(θ)) 4/(1-2sin(θ))

Cardioids

3+3cos(θ) 2+2sin(θ) 3-3cos(θ) 2-2sin(θ)

Limacons

2+3cos(θ) 1+2sin(θ) 2-3cos(θ) 1-2sin(θ)

Lemniscates

√(4sin(2θ)) √(4cos(2θ))

Butterfly curve

e^sin(θ)-2cos(4θ)+sin((2θ-π)/24)^5 dom=(0, 12π) 🔍+ 1 🔍