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

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

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

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

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

Practice: Evaluating Rational Functions #3) #4)

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:

Number Lines and Rational Equations [1] [2]