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Ask AI: Identify the following is either y-axis or origin symmetry or neither,f(x)=X²+3/X²-2

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Question: Identify the following is either y-axis or origin symmetry or neither,f(x)=X²+3/X²-2

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The function f(x) = (x²+3) / (x²-2) does not have y-axis symmetry or origin symmetry, so it is considered neither. Symmetry about the y-axis means that for every point (x, y) on the graph, the point (-x, y) is also on the graph. This happens when a function satisfies the condition f(-x) = f(x) for every x in the domain. In your case, substituting -x into the function doesn't yield the same result, meaning the function is not symmetrical about the y-axis. Symmetry about the origin means that for every point (x, y) on the graph, the point (-x, -y) is also on the graph. This happens when a function satisfies the condition f(-x) = -f(x) for every x in the domain. In your case, substituting -x into the function doesn't yield the negative of the original function, meaning it's not symmetrical about the origin either.

Aug. 22, 2023, 3:37 p.m.

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