Skills Practice Skills Practice for Lesson 4.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name Date Up, Up, and Away! Solving and Graphing Inequalities in One Variable Vocabulary Provide an example of each term. 1. inequality 2. inequality symbol 3. compound inequality. graph of an inequality 5. solution of an inequality Problem Set Write an inequality to represent each situation. 1. The temperature in March is greater than or equal to 5 degrees Fahrenheit. Let x represent the temperature in March. x 5 2. May s textbook weighed greater than 7 pounds. Let x represent the weight of May s textbook. 3. It took Chase less than 3 hours to complete his homework. Let x represent the amount of time it took Chase to complete his homework.. Marissa slept for 8 hours or less. Let x represent the number of hours Marissa slept. Chapter Skills Practice 361

2 Write a compound inequality to represent each situation. 5. To ride a rollercoaster, your height must be greater than or equal to 8 inches, and less than or equal to 78 inches. Let x represent the range of heights that are permitted on the rollercoaster. 8 x To avoid an extra charge for your airline luggage, your bag must weigh less than 50 pounds. Your bag weighs greater than 0 pounds. Let x represent the weight of your luggage that will avoid an extra charge. 7. The recommended ages for a board game are greater than and less than or equal to 12. Let x represent the recommended ages for the board game. 8. A recipe serves greater than or equal to 2 people, but fewer than 8 people. Let x represent the number of people the recipe will serve. Write the inequality for each graph shown. 9. x Chapter Skills Practice

3 Name Date Solve each inequality and graph the solution x < 12 x x > x x < x 6 < 31 Chapter Skills Practice 363

4 2. 3x x x x 12 < x 18 < 7 36 Chapter Skills Practice

5 Skills Practice Skills Practice for Lesson.2 Name Date Moving a Sand Pile Relations and Functions Vocabulary Match each definition to its corresponding term. 1. an indication that a group of numbers is part of a set a. dependent variable 2. the variable that represents the input value of a function b. domain 3. the set of all output values for a function c. function. the variable that represents the output value of a function d. independent variable 5. any set of ordered pairs e. input 6. a relation in which for every input there is exactly f. output one output 7. the set of all input values for a function g. range 8. the second coordinate of an ordered pair in a relation h. relation 9. the first coordinate of an ordered pair in a relation i. set notation Problem Set Identify the inputs and outputs of each relation. 1. Relation: ( 3, 2), (2, 3), (, 0), (5, 5) inputs: 3, 2,, 5; outputs: 2, 3, 0, 5 2. Relation: (0, 1), (1, 2), (2, 3), (3, ) Chapter Skills Practice 365

6 3. Relation: ( 2, 2), (2, 1), (3, 0), (5, 3), (5, ). Relation: ( 3, 1), ( 2, 0), ( 1, 3), ( 1, 0), (0, 1) 5. Relation: (, 11), (5, 18), (6, 25), (7, 32), (8, 39) 6. Relation: (10, 1), (11, 6), (12, 11), (13, 16), (1, 21) 7. Relation: (, 2), (, 6), ( 7, 9), ( 7, 11), ( 8, 15) 8. Relation: (1, 1), (2, 19), (2, 2), (3, 26), (3, 31) Determine if each relation is a function. 9. Relation: ( 2, 2), (3, 2), (, 1), (5, 2) This relation is a function because each input has only one output. 10. Relation: (3, 0), (, 3), (, ), (6, 7) 11. Relation: (3, 3), (, 1), (, 6), (5, 0), (7, 5) 12. Relation: ( 1, 2), (2, 3), (3, 0), (, 1), (5, 0) 13. Relation: (, 7), (, ), ( 2, 1), ( 1, 2), (5, 10) 1. Relation: (1, 8), (1, 8), (2, 11), (3, 5), (9, 6) 15. Relation: ( 1, ), (, 10), (1, 10), (20, 1), (21, 20) 16. Relation: ( 5, 0), (, 3), ( 3, 5), ( 2, 7), ( 1, 0) 366 Chapter Skills Practice

7 Name Date If the relation is a function, identify the domain and range. If the relation is not a function, explain why. 17. Relation: ( 2, 5), (0, 7), (2, 9), (, 11), (6, 13) The relation is a function. The domain is { 2, 0, 2,, 6}. The range is {5, 7, 9, 11, 13}. 18. Relation: ( 5, 0), (, 1), ( 3, 2), ( 2, 3), ( 1, ) 19. Relation: (0, 10), (0, 11), (1, 1), (2, 16), (3, 18) 20. Relation: (13, 2), (15, 8), (17, 1), (19, 20), (21, 26) 21. Relation: (1, 6), (2, 5), (3, 12), (, 19 ), (5, 26) 22. Relation: (6, 9), (9, 11), (9, 1), (13, 28), (19, 30) 23. Relation: (11, 8), (12, 7), (13, 6), (1, 6), (15, ) 2. Relation: ( 5, 0), ( 3, 8), ( 1, 8), (0, 5), (1, 6) Identify the independent and dependent variables in each situation. 25. The cost in dollars, c, to rent an inflatable bouncer for any number of days, d, is represented by the equation c 85 30d. The independent variable is the number of days the inflatable bouncer is rented. The dependent variable is the total cost in dollars. Chapter Skills Practice 367

8 26. An employee at a clothing store can fold n shirts in t minutes, which is represented by the equation t 3n A sketch artist can draw s sketches in t minutes, which is represented by the equation t 15s The total cost, c, in dollars that Zoe charges to wrap p presents is represented by the equation c 8 2p. 29. The number of oranges remaining, r, can be represented by the equation r 30 n, where n is the number of oranges eaten. 30. The number of empty theater seats, s, can be determined by the equation s 2000 t, where t is the number of tickets purchased. 368 Chapter Skills Practice

9 Skills Practice Skills Practice for Lesson.3 Name Date Let s Bowl! Evaluating Functions, Function Notation, Domain, and Range Vocabulary Write the term from the box that best completes each statement. domain evaluate a function function function notation range 1. To is to replace the variable with the given value and calculate the result. 2. A(n) is a relation in which every input has exactly one output. 3. A method of writing functions such that the dependent variable is replaced with the name of the function is called.. The is the set of all output values of a function. 5. The is the set of all input values of a function. Problem Set Use function notation to write an equation for each situation. 1. You decide to hit balls at a golf range. You rent a club for $5 and the cost of each ball is $0.10. Write a function f that represents the total cost in dollars to hit x golf balls. f(x) x 2. You and your friends go ice skating. Because you don t own ice skates, you need to rent them for $7.50. Each hour of skating costs $2.50. Write a function f that represents your total cost in dollars if you skate for x hours. 3. Dominic gives Blake a 5-meter head start in a race. Blake runs 11 meters in one second. Write a function f that represents Blake s position in meters in the race after x seconds. Chapter Skills Practice 369

10 . To do household repairs, a carpenter charges a fixed fee of $30 plus $15 for each hour that he works. Write a function f that represents the total charge in dollars for x hours of work. Evaluate each function at the specified value. 5. f(x) x 13 at x 1 6. f(x) 6x at x 12 f( 1) f(x) 18 x at x 9 8. f(x) x 5 at x f(x) 25 x at x f(x) 11x 8 at x f(x) x 15 at x f(x) x 9 at x 0 8 Determine the corresponding range of each function for the given domain. 13. f(x) 5x 1. f(x) 10 x Domain: {3,, 5, 6} Domain: {9, 10, 11, 12} f(3) 5(3) 15 f() 5() 20 f(5) 5(5) 25 f(6) 5(6) 30 Range: {15, 20, 25, 30} 370 Chapter Skills Practice

11 Name Date 15. f(x) x f(x) 12x 2 Domain: {2,, 6, 8} Domain: 1 3, 1, 2 2, f(x) 3 5x 18. f(x) x 20 Domain: {any real number} Domain: {any real number} 19. f(x) 3x f(x) x 5 2 Domain:, 25, 5, Domain: { 1, 0, 1, 2} Chapter Skills Practice 371

12 Use function notation to write an equation for each situation. Then use the equation to answer the question. 21. A moving company charges a fixed fee of $100 for a moving truck plus $35 for each mover that is hired. Write a function f that represents the total cost in dollars if a person hires x movers. What is the total cost if a person hires movers? f(x) x f() () If a person hires movers, the total cost is $ Your little brother is having a party at the local zoo. The zoo charges a party fee of $50 plus $5 for each guest. Write a function f that represents the total cost in dollars for x guests. What is the total cost for 13 guests? 23. It takes Mrs. Won 20 minutes to get her desk ready to grade homework. It takes her 10 minutes to grade each page of homework. Write a function f that represents the total time, in minutes, that Mrs. Won takes to grade x pages of homework. How long does it take her to grade 25 pages of homework? 2. It takes Eric 3 minutes to find each item he needs at the grocery store, and a set time of 12 minutes to purchase all his items. Write a function f that represents the total time, in minutes, Eric will spend at the grocery store if he needs x items. How long will Eric be at the grocery store if he needs 30 items? 372 Chapter Skills Practice

13 Skills Practice Skills Practice for Lesson. Name Date Math Magic The Distributive Property Vocabulary Explain the similarities and differences between each set of terms. 1. common factor and greatest common factor 2. combine like terms and simplify 3. terms and like terms. distributive property and factoring Chapter Skills Practice 373

14 Problem Set Use the distributive property to simplify each expression. 1. 3(9 1) 2. 8(12 7) 3. 3(9) 3(1) (2x 5) 6. 7(3x 12) x x 7 Use the distributive property to factor the greatest common factor from each algebraic expression x x 26x 39 13(2x) 13(3) 13(2x 3) x x x x x x Chapter Skills Practice

15 Name Date Use the distributive property to simplify each algebraic expression x 55x x 28x 33x 55x 11(3x 5x) 11( 2x) 22x 19. 6x 36x x 2x x 81x x 0x 23. 2x 26x 2. 68x 60x Write two expressions for the total area of the two rectangles. Then calculate the total area ft 10 ft 5 ft 6(15) 90; area is 90 square feet. 6(10) 6(5) ; area is 90 square feet. Chapter Skills Practice 375

16 26. 8 m 20 m m cm 20 cm 2 cm in. 10 in. 8 in. 376 Chapter Skills Practice

17 Skills Practice Skills Practice for Lesson.5 Name Date Numbers in Your Everyday Life Real Numbers and Their Properties Vocabulary Give an example of each term. 1. rational number 2. repeating decimal 3. irrational number. real number 5. Venn diagram 6. a property of the real number system Chapter Skills Practice 377

18 7. whole number 8. natural number 9. integer 10. closure in the real number system under multiplication 11. additive identity in the real number system 12. multiplicative identity in the real number system 13. additive inverse in the real number system 1. multiplicative inverse in the real number system 378 Chapter Skills Practice

19 Name Date Problem Set Write each repeating decimal as a rational number w w w 6 w Graph the numbers on a number line. Then list the numbers from least to greatest. 9. 0,, , , 1. 98, 3, , 0.5, 0, 2. 2 Chapter Skills Practice 379

20 11. 1, 2. 56, 6, , 0.7, , Classify each real number as irrational, rational, integer, whole number, or natural number. Use all relevant terms irrational Answer each question about real numbers. If your answer is no, give an example that supports your reasoning. 23. Is every natural number an integer? Yes. Natural numbers are a certain type of integer. 2. Is every real number a rational number? 380 Chapter Skills Practice

21 Name Date 25. Is every integer a whole number? 26. Is every integer a real number? For each equation, identify the property that is used in each step (x 15) x x 30 6 Given problem Distributive Property of Multiplication Over Subtraction Divide. 2x x 16 2x x 8 Add 30 to each side. Add. Divide each side by 2. Divide (x ) 3 5 Given problem 10 x ( 3) 5 10 x 7 5 x (10 7) 5 x 17 5 x x (3 x) 1 71 Given problem 15 5x x (15 1) 71 5x x x 55 5x x 11 Chapter Skills Practice 381

22 30. (x 5) (x 5) 2 2 x x x x x 8 2x x Given problem 382 Chapter Skills Practice

23 Skills Practice Skills Practice for Lesson.6 Name Date Technology Reporter Solving More Complicated Equations Vocabulary Write a definition for each term in your own words. 1. solve an equation 2. simplify an expression Problem Set Simplify each side of the equation. Do not solve. 1. 5(3x 12) 3x 2. 18(x 2) 5x 15x 60 3x 3. 1(8 9x) 3(1 10x). 12( 7x) 2(6 11) 5. 25x 60 (13 2x) (9 15x) 1 0x Chapter Skills Practice 383

24 Determine if each given value of x is a solution to the equation. If it is not, solve for x (x 2) 30 x; x 8. 17( 2) x is a solution of the equation. 2(1x 21) x 6; x 2 7 (9x 3) x 2(20 x); x (x 7) ; x Chapter Skills Practice

25 Name Date Solve each equation x 8 1 x x 20 2x 3x 8 1 3x 6 x (x 1) 2x 1. x 3(x ) x 3(1 10x) ( 7x) 6 11x (3x 2) 2 1x x 10(2 3x) (6x 1) 3(3 x) 20. (9 11x) 5(2x 20) Chapter Skills Practice 385

26 Write an equation to represent each situation. Then use the equation to answer the question. 21. Cody is trying to decide where to take a trip. He wants to compare his total flight and hotel costs between two destinations. If he travels to San Diego, his flight will cost $250 and his hotel will be $130 each night. If he travels to Philadelphia, his flight will cost $130 and his hotel will be $190 each night. How many nights would he need to stay in each city for the cost to be equal for both trips? Trip to San Diego: x Trip to Philadelphia: x x x x x 120 x 2 If he stayed in each city for 2 nights, the trips would cost the same amount. 22. Your aunt is deciding between two different babysitters. Ashley charges $18 plus an additional $8 per hour. Mark charges $10 plus an additional $10 per hour. For how many hours of babysitting would both sitters cost the same? 23. Devin is deciding between two trash pickup services. Rubbish Removers charges a monthly fee of $8 plus an additional $0.10 per pound of garbage. Drake s Disposal doesn t charge a monthly fee, but charges $0.20 per pound of garbage. For how many pounds of garbage would the monthly cost of both companies be the same? 386 Chapter Skills Practice

27 Name Date 2. Daniela is buying a new mattress. Sleep Tight charges $800 for the mattress she likes, and they charge a delivery fee of $2 per mile. Best Bedding has the same mattress for less at $650, but they charge a higher delivery fee of $5 per mile. For what delivery distance is the cost of the mattress the same for both furniture stores? 25. Ken can choose between two different cell phone plans. Nationtalk Wireless charges $5 per month and gives 500 free minutes. They charge $0.02 for each additional minute. Virtual Talk s plan charges $50 per month and gives 600 free minutes, but charges $0.30 for each additional minute. How many minutes would Ken need to use both plans for his monthly bill to be the same? 26. Jenna and Michelle are in a race. Jenna gives Michelle a 10-meter head start. They both start the race at the same time. If Jenna runs 5 meters in one second, and Michelle runs meters in one second, how many seconds after they start running will they be at the same position? Chapter Skills Practice 387

28 388 Chapter Skills Practice

29 Skills Practice Skills Practice for Lesson.7 Name Date Rules of Sports Solving Absolute Value Equations and Inequalities Vocabulary Complete each sentence with a term from the box. absolute value opposite tolerance 1. The of a number is the number that is the same distance from zero but on the other side of zero on a number line. 2. The of a number is the distance between zero and the point that represents the number on a number line. 3. A is the amount by which a quantity is allowed to vary from the normal or target quantity. Problem Set Determine the absolute value of each number Chapter Skills Practice 389

30 Calculate the distance between the numbers by writing and simplifying an absolute value expression. 9. Distance between 9 and Distance between 11 and 11. Distance between 3 and Distance between 15 and Distance between 6 and Distance between 23 and Distance between 81 and Distance between 30 and 7 Solve the absolute value equation. 17. x 19 5 x 19 5 or x x 30 x 2 x x Chapter Skills Practice

31 Name Date 20. 5x x x x x Chapter Skills Practice 391

32 Solve each absolute value inequality and graph your solution on a number line. 25. x 8 < 6 6 < x 8 < 6 2 < x < x 5 < x x x Chapter Skills Practice

33 Name Date 30. x x 6 1 > x 7 3 > 1 Chapter Skills Practice 393

34 39 Chapter Skills Practice