Question

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

f(x)= x+|x|.

Answer 1

$f(x)= x+|x|.$

As $|x|=\{\begin{matrix} x & \text{if }x\geq0, \\ -x & \text{if }x<0, \end{matrix}$

we have:

$f(x)=\{\begin{matrix} x+x & \text{if }x\geq0, \\ x+(-x) & \text{if }x<0, \end{matrix}$

$f(x)=\{\begin{matrix} 2x & \text{if }x\geq0, \\ 0 & \text{if }x<0, \end{matrix}$