Rational Functions

Rational Functions

1. Discontinuities

   • Infinite Discontinuity
     • Vertical Asymptote
   • Removable Discontinuity
     • Hole

2. Behavior near vertical asymptotes

   • • As x ---> 1- ; y ----> -∞
       • As x ---> 1+ ; y---> ∞

3. Reciprocal Transformations

   • • As f(x) increases, g(x) decreases and vice versa.

4. ·

   • f(x) and g(x) are polynomials
   • Domain
     • D: {x ∈ R| g(x) ≠ 0}
   • Zeroes
     • Zeroes of f(x) if h(x) is simplified
   • y-intercepts
     • Value of h(x) when x = 0
       • h(x) is in simplified form
       • 0 ∈ D

5. Rational Inequalities

   • • • • x ∈ (-∞, -4) ∪ [-1, 2] ∪ (3, ∞)

6. End Behavior Asymptotes

   • Reference line or curve for very large values of a function
   • Also known as oblique asymptotes

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