Question

The range of the function $f\left(x\right)=\frac{x+2}{|x+2|}$ is

Answer 1

Given function is $f\left(x\right)=\frac{x+2}{|x+2|}$
When $x>-2,$ then $f\left(x\right)=\frac{x+2}{x+2}=1$
When $x<-2,$ then $f\left(x\right)=\frac{x+2}{-(x+2)}=-1$
Hence, the range of the function is $\{-1,1\}$.