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If f(x) is an odd function, which statement about the graph of f(x) must be true?

It has rotational symmetry about the origin.
It has line symmetry about the line y = –x.
It has line symmetry about the y-axis.
It has line symmetry about the x-axis.

User Mehrmoudi
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2 Answers

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Answer: Choice A. It has rotational symmetry about the origin.

Rotational symmetry about the origin means the point (x,y) on the function curve rotates to (-x,-y) which is also on the curve as well.

For instance, the point (2,8) is on the odd function f(x) = x^3, and so is the point (-2,-8).

Going from (2,8) to (-2,-8) is a rotation of 180 degrees around the origin.

If f(x) is an odd function, then f(-x) = -f(x) for all x in the domain.

User Olivier A
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5 votes

Answer:The correct answer is A) It has rotational symmetry about the origin.

Explanation:

User ThisSuitIsBlackNot
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