Question

Find domain and range of the real function given by $f\left(x\right)=\{\begin{array}{cc}1-x,& x<0\\ 1,& x=0\\ x-1,& x>0\end{array}$, Also, draw its graph.

Answer 1

For x>0, x-1>-1 and for x<0, $-x>0\Rightarrow x>1$

Hence, for $xϵR,f\left(x\right)>-1$

Domain = Set of real numbers

Range = Set of real numbers > -1

The table for given function is as follows:

$\begin{array}{cccccccccc}x& -4& -3& -2& -1& 0& 1& 2& 3& 4\\ y& 5& 4& 3& 2& 1& 0& 1& 2& 3\end{array}$

Now, plot all the points on a graph paper which are shown below: