Vocabulary. Term Page Definition Clarifying Example. combined variation. constant of variation. continuous function.

Transcription

1 CHAPTER Vocabular The table contains important vocabular terms from Chapter. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. combined variation Term Page Definition Clarifing Eample constant of variation continuous function direct variation discontinuous function etraneous solution inverse variation 1 Algebra

2 CHAPTER Vocabular The table contains important vocabular terms from Chapter. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. combined variation constant of variation continuous function Term Page Definition Clarifing Eample A relationship containing both direct and inverse variation. The constant k in direct, inverse, joint, and combined variation equations. A function whose graph is an unbroken line or curve with no gaps or breaks. k, where k is the z constant of variation 5 constant of variation ART: a07se_c0l01_t01] direct variation discontinuous function A linear relationship between two variables, and, that can be written in the form k, where k is a nonzero constant. A function whose graph has one or more jumps, breaks, or holes. c r [ART: al07se_c1stp_t01] etraneous solution 00 A solution of a derived equation that is not a solution of the original equation. To solve, square both sides;. Check is false; so is an etraneous solution. inverse variation 570 A relationship between two variables, and, that can be written in the form k, where k is a nonzero constant and 0. [ART: a07se_c0l01_t0] 1 Algebra

3 CHAPTER VOCABULARY CONTINUED Term Page Definition Clarifing Eample joint variation radical function radical inequalit equation eponent epression function inequalit square-root function 17 Algebra

4 CHAPTER VOCABULARY CONTINUED Term Page Definition Clarifing Eample joint variation 570 A relationship among three variables that can be written in the form kz, where k is a nonzero constant. z radical function 19 A function whose rule contains a variable within a radical. f() radical inequalit 0 An inequalit that contains a variable within a radical. 7 equation 00 An equation that contains one or more epressions. 1 eponent 11 An eponent that can be epressed as m n such that if m and n m are integers, then b n n b m n b m. 1 1 epression 577 An algebraic epression whose numerator and denominator are polnomials and whose denominator has a degree 1. 1 function 59 A function whose rule can be written as a epression. f() 1 inequalit 0 An inequalit that contains one or more epressions. 1 square-root function 19 A function whose rule contains a variable under a square-root sign. f() 17 Algebra

5 CHAPTER Chapter Review -1 Variation Functions 1. The cost c to fill a sandbo varies directl as the depth of the sand s. If a sandbo filled with inches of sand cost $0 to fill, what is the cost to fill a sandbo to a depth of 9 inches?. The time t in hours needed to paint a house varies inversel with the number of painter s p. If painters can paint a 000 square foot house in hours, how man hours will it take 1 painters to paint the house? - Multipling and Dividing Rational Epressions Simplif. Identif an -values for which the epression is undefined Multipl or divide. Assume that all epressions are defined Adding and Subtracting Rational Epressions Add or subtract. Identif an -values for which the epression is undefined Algebra

6 CHAPTER Chapter Review -1 Variation Functions 1. The cost c to fill a sandbo varies directl as the depth of the sand s. If a sandbo filled with inches of sand cost $0 to fill, what is the cost to fill a sandbo to a depth of 9 inches?. The time t in hours needed to paint a house varies inversel with the number of painter s p. If painters can paint a 000 square foot house in hours, how man hours will it take 1 painters to paint the house? $10 1 hours - Multipling and Dividing Rational Epressions Simplif. Identif an -values for which the epression is undefined ; 1 1 ; ; 5,1 5 Multipl or divide. Assume that all epressions are defined ( 5) ( ) ( ) ( )( 7) - Adding and Subtracting Rational Epressions Add or subtract. Identif an -values for which the epression is undefined ; ( ; ) ( ) ( ) ( ; ) 10 Algebra

7 CHAPTER REVIEW CONTINUED 1. A hot air balloon traveled from Austin, TX to a private island. The balloon averaged 10 mi/h. On the return trip the balloon averaged 1 mi/h. To the nearest mile per hour, what is the balloons average speed for the entire trip? - Rational Functions Identif the zeros and asmptotes of each function. Then graph. 1. f() 9 1. f() 9-5 Solving Rational Equations and Inequalities Solve each equation Mart and Carla Johnson work on refinishing tables. Working alone Carla can complete a table in 7 hours. If the two work together, the job takes 5 hours. How long will it take Mar to refinish the table working alone? 11 Algebra

8 CHAPTER REVIEW CONTINUED 1. A hot air balloon traveled from Austin, TX to a private island. The balloon averaged 10 mi/h. On the return trip the balloon averaged 1 mi/h. To the nearest mile per hour, what is the balloons average speed for the entire trip? 10.9 mi/hr - Rational Functions Identif the zeros and asmptotes of each function. Then graph. 1. f() 9 1. f() 9 zeros:, ; vertical asmptote: ; horizontal asmptote: none zeros: 0; vertical asmptote:, ; horizontal asmptote: 0-5 Solving Rational Equations and Inequalities Solve each equation , no solution 5 1. Mart and Carla Johnson work on refinishing tables. Working alone Carla can complete a table in 7 hours. If the two work together, the job takes 5 hours. How long will it take Mar to refinish the table working alone? 17 1 hours 11 Algebra

9 CHAPTER REVIEW CONTINUED - Radical Epressions and Rational Eponents Simplif each epression. Assume that all variables are positive z 9 1. a Write each epression in radical form, and simplif (15) Write each epression b using eponents In an eperiment involving bacteria growth, the initial population is 50. The growth of the population can be modeled b the t 50 function n(t ) 50, where n is the number of bacteria and t is the time in hours. Based on this model, what is the population of bacteria after weeks? -7 Radical Functions Graph each function, and identif its domain and range. 9. f() 0. f() 1 1 Algebra

10 CHAPTER REVIEW CONTINUED - Radical Epressions and Rational Eponents Simplif each epression. Assume that all variables are positive z 9 1. a 5 5 a a Write each epression in radical form, and simplif (15) Write each epression b using eponents (100) 5. In an eperiment involving bacteria growth, the initial population is 50. The growth of the population can be modeled b the t 50 function n(t ) 50, where n is the number of bacteria and t is the time in hours. Based on this model, what is the population of bacteria after weeks?,55 bacteria -7 Radical Functions Graph each function, and identif its domain and range. 9. f() 0. f() 1 D: { 0} R: { } D: all real numbers R: all real numbers 1 Algebra

11 CHAPTER REVIEW CONTINUED 1. Oil is draining from a tank connected to two pipes. The speed f in feet per second at which oil drains through the first pipe can be modeled b f() (, ) where is the depth of the oil in the tank in feet. The graph of the corresponding function for the second pipe is a translation of f 5 units right. Write a corresponding function g, and use it to estimate the speed at which oil drains through the second pipe when the depth of the water is 1 ft.. Use the description to write the square-root function g. The parent function f() is verticall stretched b a factor of and then translated units left and units up. Graph each function, and identif its domain and range Solving Radical Equations and Inequalities Solve each equation a a 1 Algebra

12 CHAPTER REVIEW CONTINUED 1. Oil is draining from a tank connected to two pipes. The speed f in feet per second at which oil drains through the first pipe can be modeled b f() (, ) where is the depth of the oil in the tank in feet. The graph of the corresponding function for the second pipe is a translation of f 5 units right. Write a corresponding function g, and use it to estimate the speed at which oil drains through the second pipe when the depth of the water is 1 ft.. Use the description to write the square-root function g. The parent function f() is verticall stretched b a factor of and then translated units left and units up. g() ( ; ) 1 ft/s g() Graph each function, and identif its domain and range... 1 D: { 0} R: { } D: { } R: { 0} - Solving Radical Equations and Inequalities Solve each equation a a 0 1 Algebra

13 CHAPTER REVIEW CONTINUED. The formula d w 0.0 relates the 7 average diameter d of a cultured pearl in millimeters to its weight w in carats. To the nearest tenth of a carat, what is the weight of a cultured pearl with an average diameter of 9 mm? Solve each inequalit Algebra

14 CHAPTER REVIEW CONTINUED. The formula d w 0.0 relates the 7 average diameter d of a cultured pearl in millimeters to its weight w in carats. To the nearest tenth of a carat, what is the weight of a cultured pearl with an average diameter of 9 mm? 5. carats Solve each inequalit Algebra

15 CHAPTER Big Ideas Answer these questions to summarize the important concepts from Chapter in our own words. 1. Eplain how to multipl and divide epressions.. Eplain how to add and subtract epressions.. Eplain how eponents and radicals are related.. Eplain how to solve a radical equation. For more review of Chapter : Complete the Chapter Stud Guide and Review on pages 1 of our tetbook. Complete the Read to Go On quizzes on pages 09 and 7 of our tetbook. 15 Algebra

16 CHAPTER Big Ideas Answer these questions to summarize the important concepts from Chapter in our own words. 1. Eplain how to multipl and divide epressions. Answers will var. Possible answer: First factor an epression that needs to be factored. Multipl epressions like ou multipl fractions, multipling the numerators and the denominators. You divide epressions b multipling b the reciprocal of the second fraction.. Eplain how to add and subtract epressions. Answers will var. Possible answer: Rewrite epressions with a common denominator. Then add and subtract the epressions in the same wa as ou add or subtract fractions: add or subtract the numerators and keep the denominator the same. Then simplif.. Eplain how eponents and radicals are related. Answers will var. Possible answer: The denominator of a fractional 5 eponent is the inde of a radical. For eample: a 5 a. If the eponent is a fraction such as / it indicates that the denominator is raised to the numerator power. For eample: a a.. Eplain how to solve a radical equation. 1 Answers will var. Possible answer: Isolate the radical epression to one side of the equation and raise both sides of the equation to an eponent that will eliminate the radical. For eample: if 10, then square both sides because the square will eliminate the square root. For more review of Chapter : Complete the Chapter Stud Guide and Review on pages 1 of our tetbook. Complete the Read to Go On quizzes on pages 09 and 7 of our tetbook. 15 Algebra