,?...?, the? or? s are for any holes or vertical asymptotes.

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1 Name: Period: Pre-Cal AB: Unit 14: Rational Functions Monday Tuesday Block Friday /19 0 end of 9 weeks Graphing Rational Graphing Rational Partial Fractions QUIZ 3 Conic Sections (ON Friday s Quiz) 4 Unit 14 TEST (Graphing, Partial fractions, comple fractions) Lesson #1: Graphing Rational Functions I can graph a rational function. state all vertical asymptotes. state all horizontal or slant asymptotes. find all zeros of the function state the domain and range of the function. 5/6 Conic Sections I. Finding Vertical Asymptotes, Holes, and Domain A. A vertical asymptote or hole will occur when you by. 7 DOUBLE QUIZ Conic Sections * If the term cancels out with one in the numerator, then it makes only a in the graph. Plug the value in to the reduce equation to find the y-value of the hole. *If the term does not cancel out, then it is a vertical asymptote [ = # ] B. Set the dominator = 0 and solve for.,?...?, the? or? s are for any holes or vertical asymptotes. C. The domain will be from ( ) ( ) II. Finding Zeroes. A. A zero (root) occurs when the equals. B. Set numerator = 0 and solve for. Place the zeros on the graph and any vertical asymptotes or holes. III. Horizontal and Slant Asymptotes and Range A. To get these asymptotes look at the for both and. IF the degree is: bottom >top then there is a horizontal asymptote at. bottom = top then look at the leading coefficients at the horizontal asymptote is at. top > bottom then there is NOT a horizontal asymptote but there COULD be a. To find the slant asymptote you will need to do. B. Since the range deals with the y-values, there will be a break in the range (discontinuous) when you hit either a hole or a horizontal asymptote. NOTE: You can NEVER cross a vertical asymptote but you could cross a horizontal asymptote once then it will approach the asymptote from the other side as you move to infinity. *****HINT: MAKE YOUR SELF A STEP BY STEP FLASH CARD AND MEMORIZE IT!

2 IV. Model Problems Graph each, find all holes, asymptotes, zeros, y-intercepts and state the domain. 1 f ( ) = g( ) = y = 3 4

3 3 y = y = y = + 1

4 Practice #1: Graphing Rational Functions

5

6 Practice 1B asymptote at =1. and a vertical

7 Lesson # I can Decompose polynomial fractions. I. What are Partial Fractions? A. You may recall last year working questions like: denominator making ( + 1 )( 1 ) 3 +. You would have multiplied to get a common B. This year you will start with and work backward to find II. Process to follow A. Factor just the A B. If you have only terms then write: + factor B factor 1 C. Get a common denominator then set equal to the numerator: numerator = A( factor ) + B( factor ) 1 D. Plug-in the ZERO of factor. This will make the B-component zero out and you can solve for. Do the same thing to then solve for B. E. Write your answer like how part B looks. F. If there are factors in the denominator OR a root, you will need to use A, B, and C. Eample of how to handle a double root: = + 1 ( )( ) A B C ( ) NOTE: The double root you MUST put one as a root and another as a root. YES YOU DO HAVE TO DO IT THIS WAY. III. Model Problems Write the partial fraction decomposition of each: 3 7 A B. 3 + ( + 4)

8 C D ( 1) Practice # Write the partial fraction decomposition of each: ) ) 3 3) ( + ) + 5 4) ( 1 )( + 1 ) 5) ) ( + 1) 6 7) ) 3 9) ) 5 3 ( 1) 11) ( 1) ( + 1) 1) ( + ) ( + 1) Simplify the comple numbers 13) ) ) ) ) ******REMEMBER TEST IS ON TUESDAY SO STUDY MONDAY NIGHT*********