To check for symmetry with respect to the y-axis, we replace $x$ with $-x$ in the equation. This gives us $f(-x)=\frac{4 (-x)^{2}}{(-x)^{2}+1}=\frac{4 x^{2}}{x^{2}+1}$, which is the same as the original equation. Therefore, the graph of the function is symmetric
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