Find if the following graphs are symmetric with respect to the axes or the origin

Question

A. y=2x

B. y=3x

C. y=x^4-x^2

D. y=x^4-x

Answer 1

This question is the same as asking which of the previously mentioned functions are even functions f(x)=f(-x) and which of them are odd functions f(-x)=-f(x). Even functions are symmetric with respect to the y-axis and odd functions are symmetric with respect to the origin.

It is easy to check that

A and B are odd functions and hence, they are symmetric with respect to the origin.

C is an even function and therefore, it is symmetric with respect to the y-axis.

D is neither even nor odd and hence, it does not possess any such symmetries.