# How do you determine whether the graph of g(x)=(x^2-1)/x is symmetric with respect to the origin?

Feb 11, 2017

The graph of g(x) is symmetric with respect to the origin

#### Explanation:

The graph of g(x) is symmetric with respect to the origin if

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

that's if g(x) is an odd function , then it is:

$\ast g \left(- x\right) \ast = \frac{{\left(- x\right)}^{2} - 1}{- x} = - \frac{{x}^{2} - 1}{x} \ast = - g \left(x\right) \ast$

graph{(x^2-1)/x [-5, 5, -5, 5]}