Rational Functions Definition:

1. Rational FunctionsDefinition: f(x) = polynomial polynomial Where the denominator does not = 0.

2. The simplest rational function is …………… f(x) = 1 x The reciprocal parent function.

3. Sketch the graph of What is the domain and range? Where the function has an asymptote it is undefined.

4. To FindHoles 1) Factor. 2) Reduce. • A hole is formed when a factor is eliminated from the denominator. • Set eliminated factor = 0 and solve for x. 5) Find the y-value of the hole by substituting the x-value into reduced form and solve for y. 6) Your answer is written as a point.

5. To find Vertical Asymptote(s) 1) Set reduced denominator = 0 • Solve for x =. • Your answer is written as a line.

6. To find x- intercept(s) • Set reduced numerator = 0 2) Solve for x. 3) Answer is written as a point. (#, 0)

7. To find y- intercept 1) Substitute 0 in for all x’s. • Solve for y. • Answer is a point. (0, #)

8. END BEHAVIORBOBO Big on Bottom: H.A. at y = 0 Always y = 0.

9. END BEHAVIORBOTN Big on TOP NO: No H.A. Slant Asymptote that is linear with either positive or negative slope.

10. END BEHAVIOREATS DC Exponents Are The Same: H.A. at: y = divide the leading coefficients.