Question

How do you determine whether the graph of `f(x)=1/(4x^7)` is symmetric with respect to the origin?

Answer 1

Find `f(-x) = -f(x)`, so `f(x)` is an odd function, with rotational symmetry of order `2` about the origin.

Explanation:

We find:

`f(-x) = 1/(4(-x)^7) = (-1)^7*1/(4x^7) = -1/(4x^7) = -f(x)`

So `f(x)` is an odd function.

Its graph is rotationally symmetric about the origin, with order `2`:

graph{1/(4x^7) [-10, 10, -5, 5]}