Piecewise Function
Description
Piecewise functions in a single variable can be defined in Sage with the command piecewise. For example, suppose that we wish to define the function $f$ by
(1)\begin{align} f(x) = \begin{cases} \sin x + 1, & x > 0 \\ x^2, & -1 \leq x \leq 0. \end{cases} \end{align}
Sage Cell
Code
f = piecewise([((0,oo), sin(x) + 1), ([-1,0], x^2)]); f
Options
Option
We can plot piecewise functions. Since plot uses a line plot, notice that the vertical line from $(0,0)$ to $(0,1)$ is plotted.
Code
f = piecewise([((0,oo), sin(x) + 1), ([-1,0], x^2)])
plot(f, (x,-1,3))
Option
We can find the domain of a function.
Code
f = piecewise([((0,oo), sin(x) + 1), ([-1,0], x^2)])
f.domain()
Option
We can evaluate functions at points on the domain.
Code
f = piecewise([((0,oo), sin(x) + 1), ([-1,0], x^2)])
f(0)
Tags
Primary Tags—Precalculus:Functions.
Secondary Tags—Functions: Piecewise functions.
Related Cells
None.
Attribute
Permalink: http://doc.sagemath.org/html/en/reference/functions/sage/functions/piecewise.html
Author: T. W. Judson
Date: 03 Jan 2019 22:32
Submitted by: Tom Judson
