Multiple Plots on the Same Graph

## Description

Here is an example of how to display multiple plots on one set of axes. We will plot the following polynomials:

(1)
\begin{align} P_1 &= (x - 1)(x - 2)(x - 3)\\ P_2 &= (x - 1)(x - 2)(x - 4)\\ P_3 &= (x - 1)(x - 2)(x - 5)\\ P_4 &= (x - 1)(x - 2)(x - 6)(x - 10) \end{align}

Setting each of the plots to a different variable, then adding them together to another variable and using the .show() method allows us to show multiple plots on the same set of axes.

## Sage Cell

#### Code

P1 = plot((x - 1) * (x - 2) * (x - 3), 1, 6)
P2 = plot((x - 1) * (x - 2) * (x - 4), 1, 6)
P3 = plot((x - 1) * (x - 2) * (x - 5), 1, 6)
P4 = plot((x - 1) * (x - 2) * (x - 6) * (x - 10), 1, 6)
P = P1 + P2 + P3 + P4
P.show()

## Options

#### Option

Plotting the functions in different colors is possible. A full list of built in colors can be found by evaluating sorted(colors) in a cell. To set a plot to a certain color, set the color property, with the color you want in single or double quotes after the equal sign.

#### Code

P1 = plot((x - 1) * (x - 2) * (x - 3), 1, 6, color = 'red')
P2 = plot((x - 1) * (x - 2) * (x - 4), 1, 6, color = 'blue')
P3 = plot((x - 1) * (x - 2) * (x - 5), 1, 6, color = 'purple')
P4 = plot((x - 1) * (x - 2) * (x - 6) * (x - 10), 1, 6, color = 'purple')
P = P1 + P2 + P3 + P4
P.show()

## Tags

Primary Tags—Plotting: Two-dimensional plots

Secondary Tags—Two-dimensional plots: Rectangular plots