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It is not.

If

f(x) = ax2 and g(x) = -ax2 then the separate graphs will be two quadratic curves, f being "happy" and g being "sad". But f(x) + g(x) = 0 for all x and so is the x axis, not a quadratic.

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Q: Why does it make sense that by graphing two rational functions on the same graph be the same as if you were to add them first then graph?
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