Question

Find equivalent functional definition for each of the following and draw a graph of a function.

f(x)=2x -|x| + |x-1|

Answer 1

$$x<0, f(x)=2x-(-x)-(x-1)=2x+1$$

$$0\le x<1, f(x)=2x-x-(x-1)=1$$

$$x\ge 1, f(x)=2x-x+(x-1)=2x-1$$

$$f(x)=\begin{cases} 2x+1, &x<0 \\ 1, & 0\le x<1 \\ 2x-1, & x\ge 1 \end{cases}$$