# Curve Sketching

1a) asks you to graph $y= \frac{x^3}{x^2- 1}$ which is equivalent to $y(x^2- 1)= yx^2- y= x^3$. That, in turn, is the same as $x^3- yx^2+ y= 0$. The number of solutions to $x^3- kx^2+ k= 0$ is just the number of times that graph crosses the horizontal line y= k.