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

Dec 31, 2016

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

#### Explanation:

We find:

$f \left(- x\right) = \frac{1}{4 {\left(- x\right)}^{7}} = {\left(- 1\right)}^{7} \cdot \frac{1}{4 {x}^{7}} = - \frac{1}{4 {x}^{7}} = - f \left(x\right)$

So $f \left(x\right)$ is an odd function.

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

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