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

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Answer 1 · 2017-02-11T12:48:06

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

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

$g (- x) = - g (x)$ $g(-x)=-g(x)$

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

$* g (- x) * = \frac{{(- x)}^{2} - 1}{- x} = - \frac{x^{2} - 1}{x} * = - g (x) *$ $**g(-x)** =((-x)^2-1)/(-x)=-(x^2-1)/x **=-g(x)**$

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

How do you determine whether the graph of g(x)=(x^2-1)/xg(x)=x2−1xg(x)=(x^2-1)/x is symmetric with respect to the origin?