jmc

If $x<-7$, both $x+7$ and $x-2$ are negative. So $$y=-(x+7)-(-x+2)=-9.$$ If $x\ge 2$, both $x+7$ and $x-2$ are nonnegative. So $$y=x+7-x+2=9.$$ If $-7\le x<2$, $x+7$ is nonnegative and $x-2$ is negative. So $$y=x+7-(-x+2)=2x+5.$$ Then, $2(-7)+5=-9$, and $2(2)+5=9$. The function is increasing and continuous, so all values between $-9$ and $9$ are produced, and no others. Thus the range is $y\in \boxed{[-9,9]}$.