Lesson.1 Skills Practice Name Date I Graph in Pieces Linear Piecewise Functions Problem Set Complete each table. Then, sketch a graph that represents the problem situation. 1. Rosa saved $100 to spend on vacation. For the first 3 das of her vacation she spent $0 each da. Then for the net das, she spent nothing. After those 5 das, she spent $10 each da until her savings were depleted. Time (das) Savings (dollars) 0 100 1 80 60 3 40 4 40 5 40 6 30 7 0 8 10 9 0 Savings (dollars) 90 80 70 60 50 40 30 0 10 Rosa s Vacation Spending 0 1 3 4 5 6 7 8 9 Time (das) Chapter Skills Practice 1005
Lesson.1 Skills Practice page. Belinda is saving mone for a new snowboard. She earns $30 ever 5 das she tutors. After 30 das, she takes a break from tutoring and does not earn an mone for 10 das. After those 10 das she begins tutoring again and earns $30 ever 5 das until she reaches her goal of $300. Time (das) 0 Savings (dollars) Belinda s Savings 5 10 15 0 5 30 35 Savings (dollars) 300 00 100 40 45 50 0 10 0 30 40 50 60 70 80 90 Time (das) 55 60 3. Shanise starts a new eercise program to lose weight. Before starting the program her weight is 146 pounds. She loses pounds each of the first 4 weeks of her new program. Then, for the net weeks she loses 1 pound per week. After those weeks she adds swimming to her program and again loses pounds per week for the net weeks until she reaches her goal. Time (weeks) Weight (pounds) Eercise Program Results 0 1 3 4 5 6 7 Weight (pounds) 150 140 130 8 0 1 3 4 5 6 7 8 9 Time (weeks) 1006 Chapter Skills Practice
Lesson.1 Skills Practice page 3 Name Date 4. Carlos is training for a bike race in 30 das. For the first 5 das of his training he bikes 3 miles each da. For the net 10 das he bikes 5 miles each da. For the net 10 das of his training he bikes 8 miles each da. For the last 5 das of his training he bikes 10 miles a da. Time (das) 0 5 10 15 0 5 30 Total Distance (miles) Total Distance (miles) 150 100 50 Carlos s Bike Training 0 10 0 30 Time (das) 5. Maria earns mone delivering newspapers each morning. For the first 3 das she earns $18 each da. For the net das, she takes on an additional route to cover a coworker who is out sick and earns $36 each da. For the net das she returns to her original route and earns $18 each da. Time (das) 0 1 3 4 5 6 7 Earnings (dollars) Earnings (dollars) 144 16 108 90 7 54 36 18 Maria s Paper Route 0 1 3 4 5 6 7 8 9 Time (das) Chapter Skills Practice 1007
Lesson.1 Skills Practice page 4 6. Franco saved $00 to spend at an amusement park while on vacation. For the first das of his vacation he spent $36 each da. Then for the net das, he spent nothing. After those 4 das, he staed 3 more das and spent $40 each da. Time (das) 0 Savings (dollars) Franco s Vacation Spending 1 3 4 5 6 7 Savings (dollars) 150 100 50 0 1 3 4 5 6 7 8 9 Time (das) Write a piecewise function to represent the data shown in each table. 7. f() 0 60 1 55 50 3 45 4 45 5 45 From 0 to 3: The -intercept is 60. m 5 1 1 5 55 60 5 5 5 5 1 0 1 From 3 to 6: The slope is 0. 5 45 5 m 1 b 5 5 1 60 6 45 From 6 to 9: 7 43 8 41 9 39 f() 5 5 1 60, 0 # # 3 45, 3, # 6 1 57, 6, # 9 A point is (6, 45). m 5 1 1 5 41 43 5 5 8 7 1 1 5 m( 1 ) 45 5 ( 6) 45 5 1 1 5 1 57 1008 Chapter Skills Practice
Lesson.1 Skills Practice page 5 Name Date 8. f() 0 0 3 4 6 6 9 8 1 10 1 1 1 14 18 4 18 30 Chapter Skills Practice 1009
Lesson.1 Skills Practice page 6 9. f() 0 80 1 75 70 3 65 4 64 5 63 6 6 7 61 8 60 9 58 1010 Chapter Skills Practice
Lesson.1 Skills Practice page 7 Name Date 10. f() 0 4 3 6 6 8 9 1 1 15 0 18 1 4 4 6 7 8 Chapter Skills Practice 1011
Lesson.1 Skills Practice page 8 11. f() 0 100 80 4 60 6 60 8 60 10 60 1 54 14 48 4 18 36 1. f() 0 74 1 70 66 3 6 4 64 5 66 6 68 7 60 8 5 9 44 101 Chapter Skills Practice
Lesson.1 Skills Practice page 9 Name Date Sketch a graph that represents the data shown in each table. Write a function to represent the graph. 13. f() 3 6 1 10 0 14 1 10 6 3 f() 5 4 1 14 14. f() 3 4 6 1 8 0 10 1 8 6 3 4 Chapter Skills Practice 1013
Lesson.1 Skills Practice page 10 15. f() 6 4 4 6 0 8 6 4 4 6. f() 15 5 10 10 5 15 0 0 5 15 10 10 15 5 1014 Chapter Skills Practice
Lesson.1 Skills Practice page 11 Name Date 17. f() 3 14 11 1 8 0 5 1 8 11 3 14 18. f() 3 5 4 1 3 0 1 3 4 3 5 Chapter Skills Practice 1015
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Lesson. Skills Practice Name Date Step B Step Step Functions Vocabular For each function, write a definition and give an eample. 1. step function. greatest integer (floor) function 3. least integer (ceiling) function Chapter Skills Practice 1017
Lesson. Skills Practice page Problem Set Write and graph a function to represent each problem situation. 1. An online mall assigns shipping charges based on the total value of merchandise purchased. The shipping charges are as follows: 18% for purchases more than $0 and up to and including $50, % for purchases more than $50 and up to and including $100, 14% for purchases more than $100 and up to and including $150, 1% for purchases more than $150 and up to and including $00, and 10% for purchases more than $00. f() 5 0.18, 0, # 50 0., 50, # 100 0.14, 100, # 150 0.1, 150, # 00 0.10, 00, Online Mall Shipping Charges Shipping Charge (dollars) 7 4 1 18 15 1 9 6 3 0 60 10 180 40 Purchase Amount (dollars) 1018 Chapter Skills Practice
Lesson. Skills Practice page 3 Name Date. A fundraising compan bases the profit returned to organizations on the total value of products sold. The profit returned is calculated as follows: 40% for sales more than $0 and up to and including $50, 45% for sales more than $50 and up to and including $500, 50% for sales more than $500 and up to and including $750, 55% for sales more than $750 and up to and including $1000, and 60% for sales more than $1000. Chapter Skills Practice 1019
Lesson. Skills Practice page 4 3. A theater compan offers discounts based on the value of tickets purchased. The discounts are as follows: 5% for purchases more than $0 and up to and including $0, 10% for purchases more than $0 and up to and including $40, 15% for purchases more than $40 and up to and including $60, and 0% for purchases more than $60. 100 Chapter Skills Practice
Lesson. Skills Practice page 5 Name Date 4. A small clothing compan pas its emploees a commission based on the total value of clothing sold. The commission for each sale is calculated as follows: 6% for sales more than $0 and up to and including $30, 9% for sales more than $30 and up to and including $60, 1% for sales more than $60 and up to and including $90, and 15% for sales more than $90. Chapter Skills Practice 101
Lesson. Skills Practice page 6 5. A small town calculates its local sales ta rate based on the total value of the goods sold. The local sales ta is calculated as follows: 9% for sales more than $0 and up to and including $100, 8% for sales more than $100 and up to and including $00, 7% for sales more than $00 and up to and including $300, and 6% for sales more than $300. 10 Chapter Skills Practice
Lesson. Skills Practice page 7 Name Date 6. An electronics store rewards customers with in-store reward vouchers. The value of the reward vouchers are based on the total value of merchandise purchased. The rewards are calculated as follows: 4% for purchases more than $0 and up to and including $50, 8% for purchases more than $50 and up to and including $100, 14% for purchases more than $100 and up to and including $150, % for purchases more than $150 and up to and including $00, and 18% for purchases more than $00. Chapter Skills Practice 103
Lesson. Skills Practice page 8 Write a function to represent each problem situation. Then use our graphing calculator to graph the function. 7. To encourage qualit and minimize defects, a manufacturer pas his emploees a bonus based on the value of defective merchandise produced. The fewer defective merchandise produced, the greater the emploee s bonus. The bonuses are calculated as follows: $50 for more than $0 and up to and including $100 of defective merchandise, $30 for more than $100 and up to and including $00 of defective merchandise, $10 for more than $00 and up to and including $300 of defective merchandise, and $0 for more than $300 of defective merchandise. f() 5 50, 0, # 100 30, 100, # 00 10, 00, # 300 0, 300, 60 0 400 8. A jewelr store offers reward coupons to its customers. A $ reward coupon is awarded for each $0 spent. Write a function that represents the value of reward coupons awarded for up to $100 spent. 104 Chapter Skills Practice
Lesson. Skills Practice page 9 Name Date 9. A kids bounce house charges $8 for the first hour and $ for each additional hour of platime. Write a function that represents the charges for up to 5 hours of platime. 10. A fundraising compan bases the profit returned to organizations on the total value of products sold. The profit returned is calculated as follows: $100 for sales more than $0 and up to and including $50, $5 for sales more than $50 and up to and including $500, $350 for sales more than $500 and up to and including $750, and $475 for sales more than $750 and up to and including $1000. Chapter Skills Practice 105
Lesson. Skills Practice page 10 11. An ice rink charges hocke teams for ice time to practice. The ice rink charges $10 for the first hour and $1 for each additional hour. Write a function that represents the charges for up to 5 hours. 1. Ava is participating in a walk for charit. Her sponsors agree to donate $.50 plus $.50 for each whole mile that she walks. Write a function that represents the donation amount for up to 5 miles. 106 Chapter Skills Practice
Lesson. Skills Practice page 11 Name Date Evaluate. 13. Z4.5[ 14. \5.1] Z4.5[ 5 4 15. \8.3]. Z3.[ 17. Z7.3[ 18. Z0.6[ 19. \7.9] 0. \0.03] Chapter Skills Practice 107
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Lesson.3 Skills Practice Name Date The Inverse Undoes What a Function Does Inverses of Linear Functions Vocabular Match each definition with the corresponding term. 1. inverse operation a. the combination of functions such that the output from one function becomes the input for the net function. inverse function b. working backwards or retracing steps to return to an original value or position 3. composition of functions c. a function which takes an output value, performs some operation(s) on the value, and arrives back at the original function s input value Problem Set Identif the domain and range of each relationship and the reverse relationship. Determine if the relationship and the reverse relationship are functions. 1. Each student in our school chooses his or her favorite sport. Relationship domain: students in our school Relationship range: all of the sports chosen The relationship is a function because for each student there is eactl one favorite sport. Reverse relationship domain: all of the sports chosen Reverse range: students in our school The reverse relationship is not a function because for each sport there ma be more than one student who chose it as their favorite. Chapter Skills Practice 109
Lesson.3 Skills Practice page. Each student in our school is assigned a unique student ID number. 3. Each of the 4 students in our class chooses a red, blue, orange, green, or ellow marble from a bag of assorted marbles. 4. Ever member of the basketball team is assigned a jerse number. 5. Each member of our famil chooses their favorite game for game night. 1030 Chapter Skills Practice
Lesson.3 Skills Practice page 3 Name Date 6. Each student in our class is assigned a letter grade for their final eam. Write a phrase, epression, or sentence to describe the inverse of each situation. 7. Close a dresser drawer. Open the dresser drawer. 8. Light a candle. 9. Jog 3 blocks north and 5 blocks east. 10. Open the garage door and drive out of the garage. 11. Divide a number b then add 7. 1. Multipl a number b 3 then add 1. Chapter Skills Practice 1031
Lesson.3 Skills Practice page 4 Complete each table. Write an equation to represent the relationship. Write an equation for the inverse of the problem situation. 13. One foot is equivalent to 1 inches. Feet Inches 1 1 4 3 36 4 48 5 60 Let i 5 the number of inches. Let f 5 the number of feet. i 5 1f Inverse: f 5 i 1 14. One meter is equivalent to 100 centimeters. Meters Centimeters 1 3 4 5 15. One pint is equivalent to cups. Pints Cups 4 6 8 10 103 Chapter Skills Practice
Lesson.3 Skills Practice page 5 Name Date. Four quarters is equivalent to 1 dollar. Quarters Dollars 4 3 64 18 17. Three feet is equivalent to 1 ard. Feet Yards 3 9 1 18 4 18. One US dollar is equivalent to 13 Meican pesos. Dollars Pesos 1 3 4 5 Chapter Skills Practice 1033
Lesson.3 Skills Practice page 6 Determine the inverse of each function. Graph the original function and its inverse. 19. f() 5 4 f() 5 4 5 4 5 4 4 5 f 1 () 5 4 8 6 4 0 8 6 4 4 6 8 4 6 8 0. f() 5 1 3 8 6 4 8 6 4 0 4 6 8 4 6 8 1034 Chapter Skills Practice
Lesson.3 Skills Practice page 7 Name Date 1. f() 5 1 1 8 6 4 8 6 4 0 4 6 8 4 6 8. f() 5 6 8 6 4 8 6 4 0 4 6 8 4 6 8 Chapter Skills Practice 1035
Lesson.3 Skills Practice page 8 3. f() 5 3 8 3 4 8 3 4 8 0 8 8 4 3 4 3 4. f() 5 0.5 1 9 1 8 4 1 8 4 0 4 4 8 1 8 1 1036 Chapter Skills Practice
Lesson.3 Skills Practice page 9 Name Date Determine the corresponding point on the graph of each inverse function. 5. Given that (, 5) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? The corresponding point on the graph of f 1 () is (5, ). 6. Given that (3, 1) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? 7. Given that (4, 1) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? 8. Given that (0, 8) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? 9. Given that (1, 7) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? 30. Given that (6, 0) is a point on the graph of f( ), what is the corresponding point on the graph of f 1 ( )? Chapter Skills Practice 1037
Lesson.3 Skills Practice page 10 Determine if the functions in each pair are inverses. 31. f() 5 5 1 1 and g() 5 1 5 1 5 f() 5 5 1 1 f( g()) 5 f ( 1 1 5 f( g()) 5 5 ( 1 1 5 ) 5 5 ( 1) 1 1 5 5 ) 1 1 1 g() 5 1 5 5 g(f()) 5 g(5 1 1 1) 1 g(f()) 5 (5 1 1) 5 5 5 ( 1 1 5 ) 1 5 5 The functions are inverses because f( g()) 5 g(f()) 5. 3. f() 5 8 and g() 5 1 8 1 4 33. f() 5 1 1 5 and g() 5 1 10 1038 Chapter Skills Practice
Lesson.3 Skills Practice page 11 Name Date 34. f() 5 3 and g() 5 3 3 35. f() 5 0.4 8 and g() 5.5 1 0 36. f() 5 0. 1 6 and g() 5 5 30 Chapter Skills Practice 1039
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Lesson.4 Skills Practice Name Date Taking the Egg Plunge! Inverses of Non-Linear Functions Vocabular Write a definition for each term in our own words. 1. one-to-one function. restrict the domain Problem Set Complete each table of values for the function and its inverse. Determine whether the function is a one-to-one function. 1. f() 5 1 5 f() f 1 () 1 1 3 0 5 1 7 9 1 3 1 5 0 7 1 9 The function is one-to-one because both the original function and its inverse are functions. Chapter Skills Practice 1041
Lesson.4 Skills Practice page. f() 5 6 1 1 f() f 1 () 1 0 1 1 0 1 3. f() 5 5 8 f() f 1 () 1 1 0 0 1 1 4. f() 5 4 f() f 1 () 1 0 1 1 0 1 104 Chapter Skills Practice
Lesson.4 Skills Practice page 3 Name Date 5. f() 5 3 f() f 1 () 1 1 0 0 1 1 6. f() 5 4 f() f 1 () 1 1 0 0 1 1 Chapter Skills Practice 1043
Lesson.4 Skills Practice page 4 Determine whether each function is a one-to-one function b eamining the graph of the function and its inverse. 7. f() 5 4 1 7 8. f() 5 5 8 6 4 8 6 4 8 6 4 0 4 6 8 8 6 4 0 4 6 8 4 4 6 6 8 8 The function is one-to-one because both the original function and its inverse are functions. 9. f() 5 3 10. f() 5 3 8 8 6 6 4 4 8 6 4 0 4 6 8 4 6 8 8 6 4 0 4 6 8 4 6 8 1044 Chapter Skills Practice
Lesson.4 Skills Practice page 5 Name Date 11. f() 5 6 3 1. f() 5 3 8 8 6 6 4 4 8 6 4 0 4 6 8 8 6 4 0 4 6 8 4 4 6 6 8 8 Identif each equation as linear, eponential, quadratic, or linear absolute value. Determine whether the function is a one-to-one function. 13. f() 5 9 The function is a linear function. A linear function that is not a constant function is a one-to-one function. So, the function is one-to-one. 14. f() 5 6 15. f() 5 3 1 10 Chapter Skills Practice 1045
Lesson.4 Skills Practice page 6. f() 5 5 17. f() 5 6 18. f() 5 9 1 3 Determine the equation of the inverse for each quadratic function. 19. f() 5 7 f() 5 7 5 7 5 7 7 5 6 7 5 f 1 () 5 6 7 0. f() 5 1. f() 5 6 1 11. f() 5 1 1046 Chapter Skills Practice
Lesson.4 Skills Practice page 7 Name Date 3. f() 5 4 6 4. f() 5 3 1 0 Determine the equation of the inverse for each given function. Graph the function and its inverse. Restrict the domain of the original function and the inverse so that the inverse is also a function. 5. f() 5 f() 5 5 5 5 6 5 f 1 () 5 6 8 6 4 8 6 4 0 4 6 8 4 6 8 f() 5, domain: $ 0, range: $ 0,, domain: # 0, range: $ 0, f 1 () 5, domain: $ 0, range: $ 0,, domain: $ 0, range: # 0, For the function 5 with $ 0, the inverse is 5. For the function 5 with # 0, the inverse is 5. Chapter Skills Practice 1047
Lesson.4 Skills Practice page 8 6. f() 5 1 3 8 6 4 8 6 4 0 4 6 8 4 6 8 1048 Chapter Skills Practice
Lesson.4 Skills Practice page 9 Name Date 7. f() 5 4 8 6 4 8 6 4 0 4 6 8 4 6 8 Chapter Skills Practice 1049
Lesson.4 Skills Practice page 10 8. f() 5 8 6 4 8 6 4 0 4 6 8 4 6 8 1050 Chapter Skills Practice
Lesson.4 Skills Practice page 11 Name Date 9. f() 5 8 6 4 8 6 4 0 4 6 8 4 6 8 Chapter Skills Practice 1051
Lesson.4 Skills Practice page 1 30. f() 5 5 8 6 4 8 6 4 0 4 6 8 4 6 8 105 Chapter Skills Practice