Match the graphs shown above with the functions listed below. Enter "r" for red, "g" for green, "p" for purple, "b" for blue, and "y" for yellow.

: $f(x) = \frac{1}{x}.$
: $f(x) = \frac{1}{x^2+1}.$
: $f(x) = \frac{x}{x^2-1}.$
: $f(x) = \frac{x^2}{x^2+1}.$
: $f(x) = \frac{x^3}{x^2-1}.$

Hint: Again, look for various kinds of asymptotes.