# Syntax

The graphing calculator graphs functions and parametric curves on an interval (domain), dom=(a, b). You do not have to type the domain; the graphing calculator and other graphers (now all consolidated into one Graphing Calculator) append a suitable interval to expressions automatically. You can then change the end-points as desired.

If you do not specify an interval, the graphing calculator and other graphers append dom = (-∞, ∞) or dom = (0, 2π) to function expressions depending on whether graphing using the Cartesian or polar coordinate system, respectively. For parametric expressions the calculators append dom = (0, 2π) in both Cartesian and polar graphing. You can change the endpoints as desired.

In polar or parametric cases, the specified intervals must be bounded; otherwise, 's will be replaced by some constant values.

Note: in general, this graphing calculator and the other graphers allow you to use (constant) numerical expressions such as π, 1+√(2) or other numeric expressions wherever you can use a literal number for, e.g., domain end-points, axis labels, angles, etc.

The graphing calculator recognizes x, θ, t and y as variables and is programmed to work intelligently. It automatically detects the type of expression as you type. If you insert a comma, changes occur in the relevant input panel indicating a parametric expression is being entered. Otherwise — deleting the comma — the input panel switches back to the function entering mode. The Graphing Calculator then, appropriately, replaces
• t's and θ's by x's when graphing functions using the Cartesian coordinate system.
• x's and t's by θ's when graphing functions using the polar coordinate system.
• x's and θ's by t's when graphing parametric equations in both coordinate systems.
Remark: although the variables x, θ and t are intended to be used for functions (Cartesian / polar) and parametric curves, respectively, you can still use them interchangeably.

For example, the function expression xsin(t) is internally replaced by xsin(x) or θsin(θ) depending on the selected coordinate system. similarly, the parametric expression [xsin(t), θcos(x)] is replaced by [tsin(t), tcos(t)]. Clicking anywhere on the page will replace the variables in the input box with the suitable ones as mentioned above.

Note: unless the variable y is used in an equation, the graphing calculator regards it (without replacing it) as x or θ depending on the coordinate system selected. In parametric expressions y is replaced with t internally.

## Functions

To graph a function, for example, f(x) = 3x2 + 2x + 1 type in 3x^2+2x+1

Function Graphing Calculator

Or, when graphing using the polar coordinate system, if the expression is represented by r(θ) = 2 + 2θ + 1, type in 3θ^2+2θ+1

To type θ type ..t (two dots followed by t). You can also use x for θ. All x's are internally replaced by θ when graphing functions in polar coordinate system.

Function Graphing Calculator - Polar

## Equations

To graph an equation, for example, x^3-xy+2y^2 = 5x+2y+5   just type in the equation (using the "=" sign).

Equation Graphing Calculator

## Parametric Curves

To graph a parametric curve represented, for example, by a function p(t) = [x(t), y(t)] = [sin(t), cos(t)]   for -π < t < π or equivalently, by the equations x(t) = sin(t) y(t) = cos(t) < t < π type in [sin(t), cos(t)]   dom=(-pi, pi)

Using [ ] to enclose x(t), y(t) is optional.

Parametric Graphing Calculator

Or, when graphing using the polar coordinate system, if the expression is represented by p(t) = [r(t), θ(t)] = [sin(t), cos(t)]   for < t < π or equivalently, by the equations r(t) = sin(t) θ(t) = cos(t) < t < π type in [sin(t), cos(t)]   dom=(-pi, pi)

Using [ ] to enclose r(t), θ(t) is optional.

Parametric Graphing Calculator - Polar