How to check a function is symmetry about a point and line?

What is the rotational symmetry about the point O and line of symmetry of the given figure?

Line of symmetry if a line divides a given figure into two identical halves then we say that the given figure is symmetrical about that line and the line is called the axis of symmetry or line of symmetry.

Which of the following figures have rotational symmetry about the marked point (*)? Also, find the order of rotational symmetry.

Which of the following shapes have rotational symmetry about the marked point.

What can you say about the relation between line symmetry and point symmetry?

Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?

Draw lines of symmetry for the following figures. Identify which' of them have point symmetry. Is there any relation between lines of symmetry and point symmetry?(pic)

Check whether the function has (have) y-symmetry or origin symmetry: f(x) = x^(2) sin x .

Check whether the function has (have) y-symmetry or origin symmetry: f(x) = x^(2) sin x .