Question

How do you determine whether the graph of `f(x)=1/x-x^100` is symmetric with respect to the origin?

Answer 1

See below.

Explanation:

To be symmetric with respect to the origin implies in

`f(x)=-f(-x)`

Here `f(-x)=-1/x-(-x)^100=-1/x-x^100` so

so `f(-x) ne -f(x)` and `f(x)` is not symmetric with respect to the origin.