Rational Functions p(x) and q(x) are polynomials, with

Main Characteristic: Asymptotes Asymptotes are lines (horizontal or vertical) that the function approaches for certain inputs. Horizontal: for larger and larger values of x Vertical: for inputs that get closer to a domain restriction, in this case, a value that causes division by zero.

Asymptotes Horizontal: y = k is a horizontal asymptote when n < = m. Vertical: x = c is a vertical asymptote when f(c) does not equal 0 but g(c) does equal 0.

Example 1 Asymptotes: Create a table of points: f(x) x x f(x) -1.5 1 -1.5 1 -7 1.5 -18 1.9 -106 2.5 26 3 15 10 5.375 20 4.611111 50 4.229167 100 4.112245 x

Example 2 Asymptotes: Find a few points: f(x) x f(x) -1 -6 2 20 3 15 x

Example 3 If the cost function for producing x items is given, describe the associated average cost function. Asymptotes: x