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

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Answer 1 · 2016-12-31T00:15:58

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

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]}

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