# Symmetry about the origin?

Determine whether the graph of the relation is symmetric with respect to the y axis, x axis, or the origin.

y=$$(x-3)^{3}$$

I don't know how to produce a visual of the graph with this post but it is a graph of y=$$x^{3}$$ moved 3 units to the right along the x axis. Visual examination of the graph tells me that the equation is not symmetrical about the y axis, the x axis or the origin.
Using the tests for symmetry seem to confirm this.
For y symmetry: substituting -x for x does not yield an equivalent expression.
For x symmetry: substituting -y for y does not yield an equivalent expression.
For symmetry about the origin: substituting -x for x and -y for y also does not yield an equivalent expression. I get y=$$(x+3)^{3}$$
The answer given on the answer sheet is that the expression is symmetric about the the origin. I am not seeing this.

Thanks for any replies.

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
y= (x- 3)2 is clearly not symmetric about the orgin. It is symmetric about the point (3, 0). Perhaps that was what was meant- or it is just a typo.