Given the function:
[tex]f(x)=\begin{cases}x+1;x<0 \\ 2;0\le x\le1 \\ x;x>1\end{cases}[/tex]
The given function is a piecewise function
we will draw each definition over the given domain to it
the first definition is (x+1) which is a line that will be graphed in the domain (∞,0)
To graph a line, we need two points
when x = 0, f = 1
when x = -1, f = 0
So, the graph of the line will be as follows:
The second definition is when (f(x) = 2) that will be graphed in the domain [0,1] which is a horizonatl line at f = 2
The graph of this term will be as follows:
The last definition is when ( f(x) = x )
which is a line that will be graphed in the domain (1,∞)
the graph of the line will be as shown:
The graph of the overall function will be as shown in the following picture:
