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Rational Expressions. GRAPHING. Objectives. Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes (point discontinuity) in its graph. Glossary Terms. asymptote horizontal asymptote point discontinuity rational function vertical asymptote
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Rational Expressions GRAPHING
Objectives • Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes (point discontinuity) in its graph.
Glossary Terms asymptote horizontal asymptote point discontinuity rational function vertical asymptote y-intercept
Rational Function • An equation in the form • Where p(x) and q(x) are polynomial functions and q(x)0.
When graphing rational functions • State domain • Find Vertical Asymptote(s) • Find Point of Discontinuity in the graph (HOLES) • Find Horizontal Asymptote • Find the y-intercepts & x-intercepts • Sketch
State Domain • Find Vertical Asymptote(s) • Find Point of Discontinuity in the graph Domain: (-∞,-5) U (-5,1) U (1,∞) Vertical Asymptote(s) x=1 & x=-5 Find Point of Discontinuity in the graph - none
Find Horizontal Asymptote • Compare the degree of the numerator to the degree of the denominator degree of the numerator < degree of the denominator H.A. y = 0
Find Horizontal Asymptote • Compare the degree of the numerator to the degree of the denominator degree of the numerator < degree of the denominator H.A. y = 0 degree of the numerator = degree of the denominator H.A. y = the ratio of the lead coefficients. degree of the numerator > degree of the denominator none
Find y-intercept • Substitute zero for x and find the value of the function
Sketch the graph Vertical Asymptotes Horizontal Asymptote y-intercept Plot a few points
4 • State the domain • Find Vertical Asymptote(s) • Find Point of Discontinuity in the graph Domain: (-∞,-6) U (-6,-1) U (-1,∞) Vertical Asymptote(s) x=-1 Find Point of Discontinuity at -6
Find Horizontal Asymptote • Compare the degree of the numerator to the degree of the denominator degree of the numerator = degree of the denominator H.A. y = the ratio of the lead coefficients. y = 1
Find y-intercept • Substitute zero for x and find the value of the function
Sketch the graph Vertical Asymptote Point of Discontinuity Horizontal Asymptote y-intercept Plot a few points
6 • State the Domain • Find Vertical Asymptote(s) • Find Point of Discontinuity in the graph Domain: (-∞,-4) U (-4,∞) Vertical Asymptote(s) NONE Find Point of Discontinuity at -4
Find Horizontal Asymptote • Compare the degree of the numerator to the degree of the denominator degree of the numerator > degree of the denominator H.A. there is no horizontal asymptote
Find y-intercept • Substitute zero for x and find the value of the function
Sketch the graph Point of Discontinuity y-intercept Plot a few points
Homework – day 1 • Rational Functions Worksheet 1, part A & B • Graphing Rational Function Worksheet #1-3, 5
Graphing Rational ExpressionsOblique Asymptotes To find Oblique (Slant) Asymptotes you will need to divide.
Homework – day 2 Page 405 21-43 odd