Question

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

Answer 1

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(-x)=-g(x)`

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

`**g(-x)** =((-x)^2-1)/(-x)=-(x^2-1)/x **=-g(x)**`

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