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Three points on the graph of the function $f(x)$ are $\{(0,1),(1,2),(2,4)\}$. Which equation represents $f(x)$ ?$\newline$$f(x)=(x+1)^{2}$$\newline$$f(x)=2 x$$\newline$$f(x)=2^{x}$$\newline$$f(x)=x+1$