Answer to Question #331285 in Algebra for Abdulazim Ibrahim

Question

Sketch the graph of f: x->x+|x+2| where x€R

Answer 1

$f(x)=x+|x+2|=\begin{cases} x+x+2,\ \ \text{if} \ x\geq -2 \\ x-(x+2),\ \ \text{if}\ x<-2 \end{cases} =\begin{cases} 2x+2,\quad \text{if}\ \ x\geq -2 \\ -2,\qquad \ \ \text{if}\ \ x<-2 \end{cases}$