## Syntax for Functions

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

**3x^2+2x+1**

Or, when **graphing in the polar coordinate system**, if the expression is represented by
r(θ) = **3θ ^{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**.

A polar function grapher is a **graphing software** that plots the graph of a function on a given *domain* in the polar coordinate system. The resulting graph is referred to as the **polar graph** or the **polar curve** of the function.

## Syntax for Equations

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.

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

## Syntax for Parametric Curves

A parametric equations grapher is a **graphing software** that draws the range of a function p(t) = **[f _{1}(t), ..., f_{n}(t)]** on a given

*domain*in a coordinate system. Such a graph is called the graph of the parametric equations

**, ...,**

*x*= f_{1}_{1}(t)**or the**

*x*= f_{n}_{n}(t)**parametric curve**

*represented*by the function

**p(t)**.

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)**

**[ ]**to enclose x(t), y(t) is

*optional*.

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 enclose r(t), θ(t) is

*optional*.

## Syntax for Points

A points grapher (or **coordinates plotter**) is a **graphing software** that graphs a set of **points** in a coordinate system. The **coordinates of the points** are given by ordered pairs **(a _{n}, b_{n})** where (a

_{n}, b

_{n}) can be either the

**Cartesian**or

**polar coordinates**of the points.

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}**