Explanation:
Here we need to find the graph of the function:
[tex]f(x)=\frac{2x}{x^2-1}[/tex]
So we can rewrite this function as follows:
[tex]f(x)=\frac{2x}{(x-1)(x+1)}[/tex]
By using graphing tool, we get the graph shown below. As you can see, this graph has a vertical asymptote at:
[tex]x=1 \ and \ x=-1[/tex]
This is so because the denominator can't be zero, so those values make the denominator to be zero.
Also, it has an horizontal asymptote at [tex]y=0[/tex] because the degree of the numerator is lower than that of the denominator.
