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

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Answer 1 · 2017-01-10T12:23:53

See below.

To be symmetric with respect to the origin implies in

$f (x) = - f (- x)$ $f(x)=-f(-x)$

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

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

How do you determine whether the graph of f(x)=1/x-x^100f(x)=1x−x100f(x)=1/x-x^100 is symmetric with respect to the origin?