Building and drawing a piecewise function

To draw a piecewise function you plot each piece only on its own interval, paying attention to the junction points.

Example — Construction

$f(x)=\begin{cases} x+2 & x\le -1 \\ x^2 & -1<x<2 \\ 4 & x\ge 2\end{cases}$ Domain: all of $\mathbb{R}$ (the three pieces cover $(-\infty,-1]\cup(-1,2)\cup[2,+\infty)=\mathbb{R}$). Pieces: line, parabola, constant. At the junction points $x=-1$ and $x=2$ the pieces have the same height ($1$ and $4$ respectively): the function is continuous on all of $\mathbb{R}$.

Graph of $f$: the linear piece $x+2$ for $x\le -1$, the arc of parabola $x^2$ for $-1<x<2$ and the constant $4$ for $x\ge 2$ join up without jumps.

Links

Topics: Functions and properties
Concepts: Continuity · Piecewise function
Skills: Plotting a graph