Date Lesson Text TOPIC Homework. Simplifying Rational Expressions Pg. 246 # 2-5, 7

Transcription

1 UNIT RATIONAL FUNCTIONS EQUATIONS and INEQUALITIES Date Lesson Tet TOPIC Homework Oct. 7.0 (9).0 Simplifing Rational Epressions Pg. 6 # -, 7 Oct. 9. (0). Graphs of Reciprocal Functions Pg. #,,, doso, 6, 7,, Oct.. (). Eploring Quotients of Polnomial Functions Investigation on Pg. 8 Parts A, B, E, F, G, H, I, N Oct. Oct. Oct..- cont d (). (). ()... Quotients of Polnomial Functions Pg. 6 #, a-d, Graphs of Rational Functions f ( ) a b c d Pg. 7 #, 8, 9, 0 Solving Rational Equations Pg. 8 #,,, ( 7)sodo, 8, Oct. 6 Oct. 9. (6).6 (8). Solving Rational Inequalities Using Tables QUIZ (..) Review for Unit Test Pg. 9 #,, ( 6)sodo, 9, Pg. 08 # ab,,,, b, 6, 7bc, 9, 0cd,, Oct..7 (9) UNIT TEST

2 MHF U Lesson.0 Simplifing Rational Epressions. Simplif and evaluate each of the following, where =. State an restrictions. a) 6 6 b) 8. Simplif each epression and state an restrictions. a) 0 a a a a a b) 7

3 . Simplif each epression and state an restrictions on the variables. a) a 7 a a b) Pg. 6 #, 7

4 MHF U Investigation. Graphs of Reciprocal Functions INVESTIGATION Sketch f() = + and g() =. Complete the table below CHARACTERISTIC f() = + g() = -intercepts and/or asmptotes interval(s) on which the graph is above the -ais interval(s) on which the graph is below the -ais interval(s) on which the function is increasing interval(s) on which the function is decreasing -value(s) where the -value is -value(s) where the -value is -.

5 INVESTIGATION Sketch f() = and g() =.. Complete the table below. Use a TI-8 to see how ou did. Use the window as shown below CHARACTERISTIC f() = g() = -intercepts and/or asmptotes interval(s) on which the graph is above the -ais interval(s) on which the graph is below the -ais interval(s) on which the function is increasing interval(s) on which the function is decreasing -value(s) where the -value is -value(s) where the -value is -. Pg. #,,, doso, 6, 7,,

6 SUMMARY

7 MHF U Investigation. Part I Rational Functions PART I - Use desmos to graph the following functions using the given window, then draw a sketch. Row A Row B Row C check the point at = check the point at = -

8 PART II - Describe the characteristics of the graphs ou created in PART I. zeros asmptotes domain range Continuous Everwhere? Reason As, As, As, As, As, As, End Behaviours As, As, As, As, As, As, Function? Reason

9 PART III - PART F from investigation on Page 9 (i) (ii) (iii) check the point at = check the point at = - (iv) (v) (vi) (vii) (viii)

10 PART IV - PARTS G, H, I, N from pgs Question G Functions with Holes Functions with V.A. What do ou notice about 0. f ( )? H An other functions with an Oblique Asmptote? Connection between degrees of numerator and denominator? I Horizontal Asmptote:. Oblique Asmptote: (i) HOLE: (ii) VERTICAL ASYMPTOTE: N (iii) HORIZONTAL ASYMPTOTE: (iv) OBLIQUE (SLANT) ASYMPTOTE: HW Da : Finish Parts I IV of this investigation

11 MHF U Investigation. Part II Rational Functions

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13 Da : Pg. 6 #, a-d,

14 MHF U Lesson. Rational Functions in the Form f () a b c d Propert Eample: f () -intercepts -intercepts Vertical Asmptotes Horizontal Asmptotes The two branches of the graph of a function in the form f () a b c d of intersection of the vertical and horizontal asmptotes. are equidistant from the point

15 E. Sketch the graph of f () Pg. 7 #, 8, 9, 0

16 MHF U Lesson. Solving Rational Equations ALGORITHM Factor everthing that is factorable. Epress using the Lowest Common Denominator (LCD). Set = 0 or cross multipl (eliminates step ) Eliminate the denominator b multipling both sides b the LCD. Solve for the variable. Check restrictions and eliminate an etraneous solutions. Check our answer(s). E. Solve each of the following. R a) 6 b) 6 8

17 c)

18 E. Find the equation of the oblique asmptote and determine how the curve approaches the OA as f ( ) Pg. 8 #,,, ( 7)sodo, 8,

19 MHF U Lesson. SOLVING RATIONAL INEQUALITIES Set <, >, or 0 Factor everthing that is factorable. Epress using the Lowest Common Denominator (LCD). Find an zeros using the numerator. Find an vertical asmptotes using the denominator. Construct an interval table based on the zeros and VA's and holes, if the eist Determine where f() < 0, f() > 0, f() 0 or f() 0 depending on equation from. Check our answer and state the solution. E. Solve. R a) 6 0 b) 0 ( )( ) 0

20 c) 7 Pg. 9 #,, ( 6)sodo, 9,