## Description

We will be plotting a function with vertical asymptotes using multiple plotting functions. Due to the nature of the way Sage generates graphs, not using these options will likely result in a graph with an enormous range and inaccurate function values near the asymptotes. Specifically, we will be setting `ymin`, `ymax`, and `detect_poles`.

## Sage Cell

Setting `ymin` and `ymax` prevents Sage from plotting on a range in the thousands, while setting `detect_poles=True` prevents Sage from mistakenly graphing on the asymptote (for this example, had we not set `detect_poles=True` we would have seen a line on $-2$ and $2$).

#### Code

`plot(1/(x^3 -x ), -2, 2, ymin=-5, ymax=5, detect_poles=True)`

## Options

#### Option

Showing the asymptotes with a dashed line. Simply set `select_poles='show'`. Note the single quotes around 'show' because show is not a Sage keyword.

#### Code

`plot(1/(x^3 -x ), -2, 2, ymin=-5, ymax=5, detect_poles='show')`

## Tags

Primary Tags—Plotting: Two-dimensional plots; Precalculus: Rational equations and functions

Secondary Tags—Two-dimensional plots: Rectangular plots; Rational equations and functions: Asymptotes

## Related Cells

- Plotting a Circle
- Plotting a Polygon
- Plotting an Implicit Function
- Two-Dimensional Plots
- Parametric Plots
- Line Plots
- Plotting Two-Dimensional Vector Fields
- Multiple Plots on the Same Graph
- Controlling the Viewing Window of a Plot
- Multiple Annotation Techniques for Graphing
- Occasional Issues in Polar Plotting
- Constructing Contour Plots in Sage
- Plotting Inequalities in Sage
- Plotting Systems of Linear Inequalities
- Plotting Nonlinear Inequalities in Sage
- Making log-log Plots in Sage

## Attribute

Permalink:

Author: Gregory V. Bard. *Sage for Undergraduates.* American Mathematical Society, Providence, RI, 2015. Available at http://www.gregorybard.com/Sage.html.

Date: 15 Feb 2019 01:20

Submitted by: Zane Corbiere