Graph and continuity of a piecewise function

Problem

Sketch the graph of $f(x)=\begin{cases} -1 & x<-2 \\ x+1 & -2\le x\le 2 \\ 3 & x>2\end{cases}$ and check continuity at the junctions.

Solution

The graph is: the constant $-1$ for $x<-2$, the line segment $x+1$ from $(-2,-1)$ to $(2,3)$, and the constant $3$ for $x>2$.

Junction at $x=-2$: from the left the value is $-1$; the central piece gives $f(-2)=-2+1=-1$. They coincide → continuous. Junction at $x=2$: the central piece gives $f(2)=2+1=3$; from the right the value is $3$. They coincide → continuous. The function is continuous on all of $\mathbb{R}$.

Links

Topics: Functions and properties
Concepts: Continuity · Piecewise function
Skills: Plotting a graph
Exercise types: Study of a function