HAlgebra 2: Unit 7: Chapter 9 Spring Day Date Lesson Assignment. Section 9.1: Direct, Inverse, & Joint Variation Classwork: Packet p.

Transcription

1 HAlgebra : Unit 7: Chapter Spring 0 Name RATIONAL FUNCTIONS. NC Objectives:.0 Operate with algebraic epressions (polynomial, rational, comple fractions) to solve problems..0 Model and solve problems using direct, inverse, combined and joint variation..0 Use rational equations to solve problems. a. Solve using tables, graphs, and algebraic properties. b. Interpret the constants and coefficients in the contet of the problem. c. Identify the asymptotes and intercepts graphically and algebraically. Day Date Lesson Assignment Wed. May 7 Thurs. May Fri. May Mon. May Section.: Direct, Inverse, & Joint Variation Classwork: Packet p. Section.: Graphing Inverse Variation Section.: Rational Functions & their Graphs Vertical Asymptotes Horizontal Asymptotes Multiplying & Dividing Rational Epressions Quiz on Section.-. Section.: Adding & Subtracting Rational Epressions Packet p. Packet p. & Watch Video: Handout & Packet p. 6 Study for Quiz Watch Video: Packet p. 7 Part A Watch Video: Tues. May Wed. May Thurs. May Simplifying Comple Fractions Review: Operations with Rational Epressions Section.6: Solving Rational Equations Section.6: Applications of Rational Equations Give out rubric for paper slide project Review and Comple Fractions Handout Packet p. 7 Part B Packet p. 0 Fri. May 6 Mon. May Tues. May 0 Review of Unit: Paper slide project Finish Paper slide project Review for Unit Test 7 Review: Packet p. - Unit Test 7 TBD

2 HONORS ALGEBRA VARIATION WORKSHEET. If r varies directly as s, and r when s 0, find r when s 0.. If y varies directly as, and y when, find y when 0.. If p is directly proportional to t and p when t 0, find p when t.. If y varies inversely as and y 7 when, find y when.. If y varies inversely as and y when, find y when. 6. If y varies inversely as and y when, find y when If y varies jointly as and z and y when and z, find y when and z.. If y varies jointly as and z and y 7 when and z, find y when and z.. If y varies jointly as and z and y when and z, find y when and z A fish with a mass of kg causes a fishing pole to bend cm kg directly as the mass, how much will the pole bend for a. If the amount of bending varies fish?. The mass of a copper bar varies directly as its length. If a bar long 0 cm long has a mass of approimately 0 g, find the mass of a bar 6 cm long.. The interest earned on an investment varies directly with the interest rate. If a % rate yields $ 7, what interest rate yields $?. The illumination i from a light varies inversely as the square of its distance d from an object. i ftcandles when d ft, find i when d ft.. The pressure P of a gas at a constant temperature varies inversely as the volume V. If when P 0lb/ in, find P when V 70in. V 0in. The frequency of a radio wave is inversely proportional to its wave length. If a radio wave, 0 m long has a frequency of 00 kilocycles per second, what is the length of a wave with a frequency of 00 kilocycles? 6. The area A of a triangle varies jointly as the length of its base b and the length of its corresponding altitude h. If A cm when b 0 cm and h cm, find A when b cm and h 6 cm. 7. The distance D traveled at a uniform rate varies jointly as the rate r and the time t. If D 0 when r 60 and t, find D when r 0 and t.. The area A of a parallelogram varies jointly as the length of a base b and the length of a corresponding altitude h. If A 6 when b and h, find A when b and 6 h.

3 Honors Algebra Section.: Direct, Inverse, & Joint Variation Homework I. Identify the data in each table as a direct variation or an inverse variation. Then write an equation to model the data..).).).) X Y X Y X Y X Y II. Write a function for each statement. Then solve the equation.. Find y when = 6, if y varies directly as and y = when =. 6. Find when y =, if y varies inversely as and = 6 when y = - 7. Find y when = and z =, if y varies jointly as and z and y = when z = and =. Find when y =, if y varies inversely as and = when y = 6 III. Each pair of values is from an inverse variation. Find the missing value.. (, ), (, y) 0. (, 6), (, ). (, 7), (, y). (, ), (,.). The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 0 bags to mulch 0 ft to a depth of in., how many bags do you need to mulch 00 ft to a depth of in.?

4 Graphing Rational Functions Homework Day Points of Discontinuity Find the domain, vertical asymptotes, and holes for the following rational functions.. f (). f( ). f() 7. f( ). f( ) 6 6. f( ) 7. f( ). f()

5 . f () 0 0. f( ). f(). f( ) ( ) ( )( ) Find the domain, points of discontinuity, -intercept, and y-intercept.. f( ). f( ) Domain: Vertical Asymptote: Hole: -intercept: y-intercept: Domain: Vertical Asymptote: Hole: -intercept: y-intercept:

6 6 Multiplying & Dividing Rational Epressions Perform the indicated operations. Match the problems on the left to their correct answer on the right.. 0 ) ( ) ( ) ( ) ( ) )( (

7 Honors Algebra : Part A Homework Day Adding & Subtracting Rationals Simplify each sum or difference. d d y y y... d d y.. y y 6. y y y y y y y y 0y Homework Day : Part B Solve each equation. Check each solution ( ) y y y y 6 7

8 .) The Delaware Demolition Company wants to build a brick wall to hide the area where they store wrecked cars from public view. One bricklayer can build this wall in days. Another bricklayer can do the job in days. If the company hires both of them to work together, how long will it take them to finish the wall?.) A swimming pool takes 6 hours to fill up when the drain is closed. It takes 0 hours to drain the pool. If the water is poured into the pool with the drain open, how long will it take for the pool to fill up?.) A round trip flight took hours flying time. The plane traveled the 70 miles to the city at mi/h with no wind. How strong was the wind on the return flight? Was the wind a head wind or tail wind?.) A cyclist travels km in the same time that a walker travels km. The speed of the cyclist is km more than the speed of the walker. Find the speed of the cyclist and the speed of the walker..) The denominator of a fraction is one less than twice the numerator. If 7 is added to both the numerator and the denominator, the resulting fraction has a value of 7. Find the original 0 fraction.

9 Honors Algebra Review Sheet Unit : Rational Functions. Find the vertical asymptote(s) of the graph of f() =. Find the horizontal asymptote of the graph of f() = - -6 f() = ( - )( + ). Simplify:. Simplify: What is the difference of -? Solve - = Solve - = + +. Joseph can finish cleaning his parent s house in hour, but his little brother Timmy can destroy it in hours. If little Timmy is left unattended while Joseph is cleaning the house, how long will it take him to clean it?. The variable z varies jointly with and y. When = 6 and z =, y = 0. Write an equation that relates, y, and z. 0. If y varies inversely as and one point is (,.), which of the following points satisfies this same equation? A. (6,.) B. (,.) C. (,.) D. (., ) -. Graph f() = Which of the following statements are true about the graph of f() =? I. There is a vertical asymptote at = II. There is a vertical asymptote at = III. IV. There is a discontinuity (hole) at = There is a discontinuity (hole) at =

10 . Which function is graphed? A. 0 y = - + B. 0 y = - - C. 0 y = + + D. 0 y = + -. Where does the hole in the graph of - - f() = + - occur? a. Simplify: b. Simplify: The intensity I, of light received from a source varies inversely as the square of the distance, d, from the source. If the light intensity is footcandles at 7 feet, find the light intensity at feet. Round your answer to the nearest hundredth if necessary. 7. Decide whether the data shows inverse variation. If so, find the missing value y 0-0? -. A car travels 00 miles in the same time that a freight train travels 0 miles. The speed of the car is mph more than the speed of the train. Find the speed of the car and the speed of the train.. Given the following graph and table, state the horizontal and vertical asymptotes, as well as any holes. Horizontal asymptote Vertical asymptote Holes (if any) 0

11 Possible Review Questions 0. Find the value of k that makes ( ) a factor of k.. Solve = -6. Simplify:. An object is thrown upward into the air with an initial velocity of feet per second. The formula h(t) = t 6t gives its height above the ground after t seconds. For how many seconds will the object be in the air?. If.) f ( ), what is = - f ( )?.) ANSWERS!! y = 0.).) 7.) 0 7.).) ( + - ) ( + )( -)( + 7). hours.) 6.), - z y 0 0.).).) D II, III.) 6.) B 7 =.60 6.) Horizontal asymptote y = Vertical asymptote = - Holes (if any) =.).) 7.) 0.).) = ¼ -.) a.).).).) b.) Car: 7. mi/h Train:. mi/h.