Honors Precalculus October 12-14, 2016 Mrs. Agnew

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Presentation transcript:

Honors Precalculus October 12-14, 2016 Mrs. Agnew Rational Functions Honors Precalculus October 12-14, 2016 Mrs. Agnew

Essential Question Essential Vocabulary How do you graph rational functions? Essential Vocabulary Rational Function Asymptote (vertical, horizontal, slant) Hole Intercepts

Graphs of Rational Functions The parent function of rational functions is y = 1/x What are some of the distinguishing characteristics of this graph? Prior to graphing any rational function, it is important to examine the domain of the rational function. (Remember: denominator ≠ 0)

Asymptotes Three types of asymptotes: Vertical Asymptote Horizontal Asymptote Slant/Oblique Asymptote Occur when degree of numerator is exactly one more than degree of denominator

Vertical Asymptote The graph of a function NEVER crosses a vertical asymptote. The y-values go towards ∞ or -∞ at a vertical asymptote. Vertical asymptotes occur where denominator equals zero. Check for holes first…

Holes in the Graph Hole in graph when common factor on top and bottom of fraction. Cancel the common factor and then plug in “bad” x-value to find hole. (Remember: a hole must have an x- and a y-coordinate.)

Horizontal Asymptote Horizontal asymptote is line where graph “levels off” as the x values go towards ∞ or -∞. Horizontal Asymptote Theorem Bigger exponent on top, no HA Bigger exponent on bottom, HA y = 0. If exponent same top and bottom, HA is equal to ratio of leading coefficients. Examples…

Slant Asymptote Slant asymptotes occur when degree of numerator is exactly one more than degree of denominator. Use long division to find slant asymptote. The quotient (without the remainder) is the SA. Examples…

Homework: Page 225 #14-24 even, 43, 44, 49, 50, 51, 54

Graphing Rational Functions Steps in graphing rational functions Identify horizontal/slant asymptotes (if any) Factor completely Identify holes (if any) Identify vertical asymptotes (if any) Identify intercepts Find test points and graph Examples: page 234 #8 – 44 (Even), 46, 50, 54

Homework: Worksheet Provided