Sketch the graph of \[y = \frac{5x}{x^2 -1},\] showing clearly the three asymptotes.
What are the equations of the asymptotes?
Where does the curve cross the axes?
How does the graph behave for large values of x?
Use your graph to find the number of real roots of the equation \[kx-1 = \frac{5x}{x^2 -1},\] when \(k\) is a positive constant.
What line would it be useful to sketch on your graph?
