# a function that maps half planes

Define

$H^{+}=\{z:y>0\}$

$H^{-}=\{z:y<0\}$

$L^{+}=\{z:x>0\}$

$L^{-}=\{z:x<0\}$

$f(z)=\frac{z}{3z+1}$ maps which portion onto which from above and vice-versa? I will be glad if any one tell me how to handle this type of problem? by inspection?

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