Question

I need help with a question before my test: how do I tell if a graph has rotational Symmetry if it is not an odd function and do all odd functions have point symmetry??

Answer 1

If you know that the function is not odd, you know that the graph does not have rotational symmetry

Explanation:

There is a theorem that says: "A function is odd if, and only if, its graph is symmetric with respect to the origin, or it has rotational symmetry in 180 ° with respect to the origin"

This statement is equivalent to:

If a function is odd, its graph has rotational symmetry with respect to the origin

If a graph has rotational symmetry with respect to the origin then the function is odd.

Therefore, it is impossible for the graph to have rotational symmetry with respect to the origin and the function is not odd.

Then, if you know that the function is not odd, you know that the graph does not have rotational symmetry