Question

The graph of the equation y=x^3-x is symmetric with respect to which of the following?
a) the x-axis
b) the y-axis
c) the origin
d) none of these

Answer: c

2) The graph of an odd function is symmetric with respect to which of the following?
a) the x-axis
b) the y-axis
c) the line y=x
d) none of these

Thanks

Answer 1

Oops, forgot to mention that the answer for problem 2 is d.

Answer 2

In both case I agree. In 1) the function is odd and therefore symmetric about the origin
In 2)again an odd function is symmetric about the origin, so none of the above

Definition of Odd Function

A function with a graph that is symmetric with respect to the origin. A function is odd if and only if f(–x) = –f(x).