We are asked to graph the function `y=(2x)/(x^2-1) ` :
Factoring the denominator we get:
`y=(2x)/((x+1)(x-1)) `
The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0.
The y-intercept is 0 as is the only x-intercept.
The first derivative is ` y'=(-2(x^2+1))/((x^2-1)^2) ` so the function is decreasing on its domain.
The graph:
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