Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions.

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Presentation transcript:

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:

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)

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

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:

**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:

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