1. WARM UP: Factor each completely a)b) c) d)

2. Rational Expression: Fraction of TWO polynomials (1) SIMPLIFYING c) a) b)d)

3. b) (2) MULTIPLYING and DIVIDING a)c) d)

4. (3) ADDITION and SUBTRACTION a) b) c) d)

5. EVALUATING RATIONAL FUNCTIONS 1.Substitute x-value into the function 2.Evaluate the numerator and denominator separately 3.Reduce the resulting fraction #1) #2)

6. Practice: Evaluating Rational Functions #3) #4)

7. Number Lines and Rational Equations 1) Find All Zero/ Root Values of the numerator and denominator ZEROS in the numerator = zero in the graph (y-value) ZEROS in the denominator = undefined in the graph (no y-value) 2) Write all the Zero/Undefined x-values on the number line 3) Between those x-values pick a number to substitute into function to determine if the graph (y-value) will be positive or negative REASON: Only time we can change from positive to negative value is when we have a ZERO or UNDEFINED value of the graph Example:

8. Number Lines and Rational Equations [1] [2]