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

Jan 10, 2017

See below.

#### Explanation:

To be symmetric with respect to the origin implies in

$f \left(x\right) = - f \left(- x\right)$

Here $f \left(- x\right) = - \frac{1}{x} - {\left(- x\right)}^{100} = - \frac{1}{x} - {x}^{100}$ so

so $f \left(- x\right) \ne - f \left(x\right)$ and $f \left(x\right)$ is not symmetric with respect to the origin.