Q:

Which graphs have rotational symmetry? Check all that apply

Accepted Solution

A:
Answer:Option A and C have rotational symmetry.Step-by-step explanation:The graph of odd functions have rotational symmetry about its origin.Here the first graph is a graph of f(x)=[tex]f(x)=x^3[/tex] which is an odd function bearing an exponent of 3.A function is "odd"  when we plug in any negative value in [tex]f(x)[/tex] then it gives negative of [tex]f(x)[/tex].And we also know that when a graph is mirroring about the y-axis then it is an even functions.For even functions we have reflection symmetry rather than rotational symmetry.The second graph is a graph of [tex]f(x)=-modulus (x)[/tex] which is an even function as we can see that its graph is mirroring about the y-axis.The third graph is a graph of an ellipse which is possessing  rotational symmetry.The order of symmetry of an ellipse is generally 2.Order of symmetry:The order of rotational symmetry of an object is how many times that object is rotated and fits on to itself during a full rotation of 360 degrees.So graph A and C have rotational symmetry.