Question

The graph of the function is symmetric with respect to the origin f(x)=x^6+9x

true or false?

Answer 1

to check for symmetry with origin...substitute x to -x and f(x) to -f(x)..if the equation is correct then it is symmetric with respect to origin

Answer 2

with respect to the origin can be thought of as being rotationaly symmetric (rotate it 180 degrees about the origin.)

Answer 3

also, here's a quick way... if the polynomial is of even degree (like yours) it will definitely not be odd.