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Rational Expressions

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

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  1. Rational Expressions GRAPHING

  2. Objectives • Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes (point discontinuity) in its graph.

  3. Glossary Terms asymptote horizontal asymptote point discontinuity rational function vertical asymptote y-intercept

  4. Rational Function • An equation in the form • Where p(x) and q(x) are polynomial functions and q(x)0.

  5. 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

  6. 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

  7. 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

  8. 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

  9. Find y-intercept • Substitute zero for x and find the value of the function

  10. Sketch the graph Vertical Asymptotes Horizontal Asymptote y-intercept Plot a few points

  11. 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

  12. 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

  13. Find y-intercept • Substitute zero for x and find the value of the function

  14. Sketch the graph Vertical Asymptote Point of Discontinuity Horizontal Asymptote y-intercept Plot a few points

  15. 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

  16. 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

  17. Find y-intercept • Substitute zero for x and find the value of the function

  18. Sketch the graph Point of Discontinuity y-intercept Plot a few points

  19. Homework – day 1 • Rational Functions Worksheet 1, part A & B • Graphing Rational Function Worksheet #1-3, 5

  20. Graphing Rational ExpressionsOblique Asymptotes To find Oblique (Slant) Asymptotes you will need to divide.

  21. Homework – day 2 Page 405 21-43 odd

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