A calculus problem by Ankit Nigam

If y= $f\left( x \right)$ be a real function so that $3f\left( \frac { x+y }{ 3 } \right) =f\left( x \right) \quad +\quad f\left( y \right)$ for all x,y belongs to R and $f\left( 0 \right)$ = 2 = $f^{ ' }\left( 0 \right)$ , then the graph will be a

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