Question

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.

Answer 1

Answer:It has rotational symmetry about the origin.

Explanation:

An odd function : is a function that is symmetric about the origin.

An even function : is a function that is symmetric with respect to the y-axis.

Since , f(x) is an odd function, it has rotational symmetry about the origin.

its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.

Therefore, It has rotational symmetry about the origin.

Answer 2

An odd function, by definition, is a function that is symmetric about the origin.

An even function, by definition, is a function that is symmetric with respect to the y-axis.

Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.

ANSWER: symmetric about the origin.