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Pre-Calculus

Pre-Calculus. Rational Functions. Simple Rational Functions. Appears in the following format: Has 2 asymptotes: x=h (vertical) y=k (horizontal) In order to graph: Draw the lines for the asymptotes.

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Pre-Calculus

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  1. Pre-Calculus Rational Functions

  2. Simple Rational Functions • Appears in the following format: • Has 2 asymptotes: • x=h (vertical) • y=k (horizontal) • In order to graph: • Draw the lines for the asymptotes. • Select two points on each side of every asymptote, plug into your x/y chart and graph.

  3. Simple Rational Function Practice Determine all of the asymptotes for each graph:

  4. Simple Rational Function Practice Determine all of the asymptotes ANDgraph:

  5. Need Mo Practice? • Of course you do fool! • In groups, complete #1-4 on pg. 32 of your workbook.

  6. Complex Rational Functions • Appears in the following format: • In order to graph: • Draw the lines for the asymptotes. • Select two points on each side of every asymptote, plug into your x/y chart and graph. • Asymptotes/Quirks: • Can have multiple vertical asymptotes. • Can have multiple horizontal asymptotes horizontal asymptotes. • Might have holes.

  7. Complex Rational Functions • Appears in the following format: • Asymptotes/Quirks: • Can have multiple vertical asymptotes. • How to Determine VA’s • Factor the numerator and denominator. • Determine what values would make the denominator equal to 0.

  8. Vertical Asymptote Practice

  9. Complex Rational Functions • Appears in the following format: • Asymptotes/Quirks: • Can have multiple horizontal asymptotes horizontal asymptotes. • How to Determine HA’s • Look at the degrees of the numerator and the denominator. • Follow and memorize the guide on the next slide.

  10. Horizontal Asymptote Guide • If the degree of the numerator < degree of the denominator • Then is the horizontal asymptote. • If the degree of the numerator = degree of the denominator • Then is the horizontal asymptote. • If the degree of the numerator > degree of the denominator • Then there is no horizontal asymptote.

  11. Horizontal Asymptote Practice

  12. Complex Rational Functions • Appears in the following format: • Asymptotes/Quirks: • Might have holes. • How to Find Holes • Factor the numerator and denominator. • If there is a common factor in the numerator and the denominator, set it equal to zero. Solve and the value you find is the x-coordinate of the location your hole occurs at.

  13. Diggin’ Holes Practice

  14. Putting it All Together • Appears in the following format: • In order to graph: • Draw the lines for the asymptotes. • Select two points on each side of every asymptote, plug into your x/y chart and graph. • Determine if there are holes and graph them accordingly.

  15. Graphing Practice

  16. Graphing Practice

  17. Graphing Practice

  18. Homework – Night #1 • Complete Pg. 27-28 in your workbook #1-7. • Please find: • Vertical Asymptotes • Horizontal Asymptotes • Holes

  19. Homework – Night #2 – Period 4 • Complete your assigned problem on Pg.28-30

  20. Homework – Night #2 – Period 7 • Complete your assigned problem on Pg.28-30

  21. Pre-Calculus Carousel

  22. Homework – Night #3 • Select 5 problems to complete for each of the following pages: • Pg. #32-33 • Pg. #34-35

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