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* on this site (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 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** graphing, the specified intervals must be **bounded**; otherwise, **∞**'s will be replaced by some constant values.

**Note:** this **graphing calculator** allows using **numerical expressions** such as **π**, **1+√(2)** 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.

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

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

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**.

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

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)**
**-π < t < π** type in
**[sin(t), cos(t)] dom=(-pi, pi)**

Parametric Graphing Calculator

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

To **graph a set of points** {(x_{i}, y_{i}) : i=1,...,n}
type in
**x _{1}, y_{1}; x_{2}, y_{2}; ... x_{n}, y_{n}**

Or, when graphing the points {(r_{i}, θ_{i}) : i=1,...,n} in the **polar coordinate system**, type in
**r _{1}, θ_{1}; r_{2}, θ_{2}; ... r_{n}, θ_{n}**