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

2. 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.

3. 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.

4. 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 50
100 x

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

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