checking for origin symmetry?

Question

which of the following equations has a graph that is symmetric with respect to the origin?

a) y = x + 1/x
b) y = -x^5 + 3x
c) y = x^4 -2x^2 + 6
d) y = (x-1)^3 +1
e) y = (x^2 + 1)^2 -1

I forget how you check for origin symmetry, if anyone could explain it I'd be very thankful.

Answer 1

I believe the rule for symmetry about the origin is that, if you replace x with -x and y with -y, and you can get back to the original equation, it's symmetric.

So for part a:

-y = -x + 1/-x = -1(x + 1/x)
y = x + 1/x

Seems like it would be symmetric about the origin.

But... part b seems like it would be too

-y = -(-x)^5 + 3(-x) = x^5 - 3x
y = -x^5 +3x

In fact, I think any equation y=f(x) where the powers of x are all odd (1 and -1 for a, 5 and 1 for b) and there are no numbers SHOULD be symmetric about the origin.

I don't agree that d is symmetric, but I'm pretty sure both a and b are. Are you sure you wrote a and b down correctly?

Answer 2

Aegor R, that's not true. And there can't be anymore than 1 right answer, it's a multiple choice question to be filled out on a scantron.

Answer 3

a,b,d are symmetricalabout the origin