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1 vote
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.

2 Answers

3 votes

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.

answered
User Olivier A
by
8.3k points
5 votes

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

Explanation:

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