# SAGE : Graphing

Sage has a plethora of ways to graph expressions including options to enhance the appearance of every part of the graph. To get a full list of options evaluate **help(plot)**. We'll start out with a very simple code, and add options.

## Graphing a Single Expression

**1.** Plot $y=x^2$. By default, it will plot from $x=-1$ to $x=1$.

**2.** Change the domain to $-3\le x \le3$, and change the output to $-1\le y \le 7$.

**3. **Change the line style, color, and thickness.

Other options for linestyle are ":", "-.", "None"

## Plotting Several Expressions

There are several ways to plot more than one expression.

**4.** Plot $y=x^2$ and $y=2x+3$

**Method 1:** using a list of expressions.

**Method 2:** storing the plots in variables and combining them together.

**Method 3:** Use only one graphic object, and keep adding other graphic objects to it.

## Rational Functions and Vertical Asymptotes

**5.** Graph the rational function: $y=\frac{x+2}{x^2-2x-3}$

The vertical scale is too extreme and needs to be changed.

The vertical lines are artifacts of the plotting process. These occur when the plot goes from a negative extreme value to a positive extreme value, (or visa versa) and can be removed using **detect_poles='False'**:

To show the vertical asymptotes set **detect_poles='show'**.

## Implicit Plots

**6.** Plot the conic $x^2-xy+5y^2+4x-8y=15$

## Trigonometric Plots

**7.** Graph the trigonometric function $f(x)=\sin(x-\frac{\pi}{6})+\frac{1}{2}$, and mark the $x$-axis in terms of $\pi$;

## Parametric Plots

**8. **Graph the parametric equation described by $x=(t-1)^2$ and $y=0.2\sin(\pi t)$ for $0\le t \le2$.

## Polar Graphs

Plot the polar equation $r=3+8cos(\theta)$