You can enter Cartesian and polar equations as single-valued piecewise-defined functions. Enter all of the pieces of the equation on the same line, separated by semicolons (;). You must specify a domain for each piece, and order the pieces by increasing domain values. The domains are not required to span the entire real number line, but they must not overlap. This means that you must specify domains for pieces that abut one another using interval notation so the program can tell which function defines the value for the transition point between the pieces.

The graph of a piecewise-defined function may contain internal endcaps if adjacent pieces do not evaluate to the same result at the transition points.

You can define piecewise functions of x, y, or theta (polar coordinates), but you may not mix functions of different variables in the same equation.

Piecewise functions may reference free variables (a, b, c, etc.), but all pieces must use the same value for each variable. You may specify the value of a free variable at any point in the equation, but only the first domain specification will be recognized.

**Examples**

`y=-1 {( ,0)} ; y=0 {[0,0]} ; y=1 { (0,)}` |

`r=t {[0,1]} ; r=t^2 {(1,)}` |

**Unacceptable equations**

`y=-1 {( ,0)} ; y=0 {(0,0)} ; y=1 { (0,)}` |
Null domain "(0,0)" |

`y=-x {(,0]}; y=x^2 {[0, )}` |
Overlapping domains at point 0 |

`y=x^2-x {( , 0)} ; x=y^2-y { (0, )}` |
First piece is a function of x, second a function of y |

kSoft, Inc. ksoft@graphmatica.com Last updated: Sun 11 Jun 2017