1 / 22

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.

denis
Download Presentation

Pre-Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related