1 / 18

Precalculus Lesson

Precalculus Lesson. Quiz 2.4-2.5 Today. Check: p.206 #1,3,17,23,25,31,35,41,45,49,59,61,63,67,71,77,79,91,95,103,107. Warm-up. Use the given zero to find all the zeros of the function. Answers. {2i, -2i, -1/2, 1}. Section 2.6. Date: _______

thelma
Download Presentation

Precalculus Lesson

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. PrecalculusLesson Quiz 2.4-2.5 Today Check: p.206 #1,3,17,23,25,31,35,41,45,49,59,61,63,67,71,77,79,91,95,103,107

  2. Warm-up Use the given zero to find all the zeros of the function.

  3. Answers {2i, -2i, -1/2, 1}

  4. Section 2.6 • Date: _______ • Objective: Analyze and sketch graphs of rational functions.

  5. Notes 2.6 Rational Functions and Asymptotes. • A Rational Function, where p(x) and q(x) have no common factors, can have several vertical asymptotes, but at most one horizontal asymptote. **Note—The graph may cross a horizontal asymptote, but not a vertical one!!

  6. To find a vertical asymptote; • Set the denominator equal to zero and solve for x.

  7. To find horizontal asymptotes: • Compare the degree of p(x) (the numerator) with the degree of q(x) (the denominator.)

  8. 1. Numerator degree < Denominator degree Horizontal asymptote; y=0 • Since 2<3, then y=0 is the horizontal asymptote.

  9. 2. Numerator degree = Denominator degreeHorizontal asymptote; **Note a and b represent the leading coefficients of the numerator and denominator. Since 2=2, then y=2/3 is the horizontal asymptote.

  10. 3. Numerator degree > Denominator degreeNo horizontal asymptote • Since 5>3, then there is no horizontal asymptote.

  11. Ex 1 Find the horizontal and vertical asymptotes. a) b) c)

  12. Slant Asymptotes • IF the numerator degree is exactly onemore than the denominator degree, then the function has a slant asymptote. Use synthetic or long division to find the slant asymptote.

  13. The quotient without the remainder is the slant asymptote. y=x-2 is the slant asymptote.

  14. Ex 2 Find all of the asymptotes and sketch the graph. A)

  15. Other items to find and label: • Domain –Must find first. Set Den=0 and solve to find values to exclude! • Zeros—Set the Numerator=0 and solve. Some “zeros” must be discarded because not in domain. • Hole in graph at discarded value. • Asymptotes--Reduce if necessary. • Y-coordinate for hole —evaluate reduced function at discarded value. F(discard)=??

  16. B) Find the Domain first, then reduce to find asymptotes. NOTE—There will be a hole in the graph for the factor that cancels. Label the asymptotes, zeros, and the hole in the graph.

  17. Assignments Classwork: p. 191 # 41, 47, 65 Homework(2.6): p. 190 #17-20 (matching), 26, 28, 42, 48, 62, 66, 90

  18. 333deer, 500 deer, 800 deer 1500 is the limiting size of the herd. [Horizontal Asymptote] The game commission introduces 100 deer into newly acquired state land. The population N of the herd is modeled by Where t is time in years. Find the populations when t = 5, t=10, t=25. What is the limiting size of the herd as time increases?

More Related