if the curve of f(x) is symmetric with respect to the origin, then it follows that

f(0)=0
f(-x)=-f(x)
f(x)=f(-x)
f(x) is also symmetric with respect tot he x and y-axes
f(-x)=-f(-x)

Question

if the curve of f(x) is symmetric with respect to the origin, then it follows that

f(0)=0
f(-x)=-f(x)
f(x)=f(-x)
f(x) is also symmetric with respect tot he x and y-axes
f(-x)=-f(-x)

anonymous · Answer

@robtobey

dumbcow · Answer

whats the question?  if f(x) is symmetic about origin then yes all those follow...

anonymous · Answer

no only one of those is supposed to be the answer

anonymous · Answer

Symmetry about the origin indicates the function is odd, i.e. $f(-x)=-f(x)$.

anonymous · Answer

cant it be even as well?

anonymous · Answer

It could be, but only if $f(x)=0$. An even function has the property $f(-x)=f(x)$, which also means symmetric across the y-axis. You're not told this is the case, so $f(x)$ is not necessarily 0.

anonymous · Answer

Okay, i'm going to trust you on this one, lol