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* 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 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**, **t** and **θ** as **variables** and is programmed to work intelligently. It automatically detects the type of expression as you type. If your expression contains a *comma*, changes occur in the relevant input panel indicating a **parametric** expression is being entered. Otherwise — deleting the comma, for instance — the input panel switches back to the **function** entering mode. The **Graphing Calculator** then, appropriately, replaces
*variable* **t** might be replaced by **x** or **θ** when typing a **function**, the graphing calculator will automatically correct, for example, **xan** or **θan** to **tan** (*tangent*) and **cox** **coθ** to **cot** (*cotangent*) as you *finish* typing the predefined function *tan* or *cot*. Similar thing may happen to the **x** in **exp(** — including the left parenthesis.

**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.

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

Or, when **graphing using 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 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)**

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
-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)**