1. Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions Warm-up (IN) 1.Factor, then cancel:

2. Notes! Procedure for graphing Rational Functions by hand... ~Reminder: always factor numerator and denominator completely - Find one or two key points to help with graphing - Find domain along with x- and y-intercepts - Identify holes and vertical asymptotes (must factor polynomials) - Identify horizontal asymptotes (see next slide)

3. Finding Horizontal Asymptotes Consider the degree of both the numerator and denominator... If degree y = 0 no horizontal asymptote y = quotient of two leading coefficients

4. Ex 1: Graph D: y-int: x-int: Holes: If anything cancels, then there is a hole none Vertical asymptote Horizontal asymptote: Other key points:

5. **With two vertical asymptotes, find at least 4 key points to graph in addition to x- and y-intercepts Ex 2: Graph D: Vertical asymptotes y-int: x-int: Holes: none Horizontal asymptote:

6. HW – Graphing Rational Functions wksht Out – none Summary – I understand….or…I still have questions about… Don’t forget about POW!!