Complete each table. Then, sketch a graph that represents the problem situation.

Transcription

1 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) Savings (dollars) Rosa s Vacation Spending Time (das) Chapter Skills Practice 1005

2 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 Savings (dollars) Time (das) 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 Weight (pounds) Time (weeks) 1006 Chapter Skills Practice

3 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) Total Distance (miles) Total Distance (miles) Carlos s Bike Training 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) Earnings (dollars) Earnings (dollars) Maria s Paper Route Time (das) Chapter Skills Practice 1007

4 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 Savings (dollars) Time (das) Write a piecewise function to represent the data shown in each table. 7. f() From 0 to 3: The -intercept is 60. m From 3 to 6: The slope is m 1 b From 6 to 9: f() , 0 # # 3 45, 3, # , 6, # 9 A point is (6, 45). m m( 1 ) 45 5 ( 6) Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date 8. f() Chapter Skills Practice 1009

6 Lesson.1 Skills Practice page 6 9. f() Chapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date 10. f() Chapter Skills Practice 1011

8 Lesson.1 Skills Practice page f() f() Chapter Skills Practice

9 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() f() f() Chapter Skills Practice 1013

10 Lesson.1 Skills Practice page f() f() Chapter Skills Practice

11 Lesson.1 Skills Practice page 11 Name Date 17. f() f() Chapter Skills Practice 1015

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13 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

14 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() , 0, # 50 0., 50, # , 100, # , 150, # , 00, Online Mall Shipping Charges Shipping Charge (dollars) Purchase Amount (dollars) 1018 Chapter Skills Practice

15 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

16 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 $ Chapter Skills Practice

17 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

18 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 $ Chapter Skills Practice

19 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

20 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, # 00 10, 00, # 300 0, 300, 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

21 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

22 Lesson. Skills Practice page 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

23 Lesson. Skills Practice page 11 Name Date Evaluate. 13. Z4.5[ 14. \5.1] Z4.5[ \8.3]. Z3.[ 17. Z7.3[ 18. Z0.6[ 19. \7.9] 0. \0.03] Chapter Skills Practice 107

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25 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

26 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 Chapter Skills Practice

27 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 Multipl a number b 3 then add 1. Chapter Skills Practice 1031

28 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 Let i 5 the number of inches. Let f 5 the number of feet. i 5 1f Inverse: f 5 i One meter is equivalent to 100 centimeters. Meters Centimeters One pint is equivalent to cups. Pints Cups Chapter Skills Practice

29 Lesson.3 Skills Practice page 5 Name Date. Four quarters is equivalent to 1 dollar. Quarters Dollars Three feet is equivalent to 1 ard. Feet Yards One US dollar is equivalent to 13 Meican pesos. Dollars Pesos Chapter Skills Practice 1033

30 Lesson.3 Skills Practice page 6 Determine the inverse of each function. Graph the original function and its inverse. 19. f() 5 4 f() f 1 () f() Chapter Skills Practice

31 Lesson.3 Skills Practice page 7 Name Date 1. f() f() Chapter Skills Practice 1035

32 Lesson.3 Skills Practice page 8 3. f() f() Chapter Skills Practice

33 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

34 Lesson.3 Skills Practice page 10 Determine if the functions in each pair are inverses. 31. f() and g() f() f( g()) 5 f ( f( g()) 5 5 ( ) 5 5 ( 1) ) g() g(f()) 5 g( ) 1 g(f()) 5 (5 1 1) ( ) The functions are inverses because f( g()) 5 g(f()) f() 5 8 and g() f() and g() Chapter Skills Practice

35 Lesson.3 Skills Practice page 11 Name Date 34. f() 5 3 and g() f() and g() f() and g() Chapter Skills Practice 1039

36 1040 Chapter Skills Practice

37 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() f() f 1 () The function is one-to-one because both the original function and its inverse are functions. Chapter Skills Practice 1041

38 Lesson.4 Skills Practice page. f() f() f 1 () f() f() f 1 () f() 5 4 f() f 1 () Chapter Skills Practice

39 Lesson.4 Skills Practice page 3 Name Date 5. f() 5 3 f() f 1 () f() 5 4 f() f 1 () Chapter Skills Practice 1043

40 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() f() The function is one-to-one because both the original function and its inverse are functions. 9. f() f() Chapter Skills Practice

41 Lesson.4 Skills Practice page 5 Name Date 11. f() f() 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() f() Chapter Skills Practice 1045

42 Lesson.4 Skills Practice page 6. f() f() f() Determine the equation of the inverse for each quadratic function. 19. f() 5 7 f() f 1 () f() 5 1. f() f() Chapter Skills Practice

43 Lesson.4 Skills Practice page 7 Name Date 3. f() f() 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() f 1 () 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

44 Lesson.4 Skills Practice page 8 6. f() Chapter Skills Practice

45 Lesson.4 Skills Practice page 9 Name Date 7. f() Chapter Skills Practice 1049

46 Lesson.4 Skills Practice page f() Chapter Skills Practice

47 Lesson.4 Skills Practice page 11 Name Date 9. f() Chapter Skills Practice 1051

48 Lesson.4 Skills Practice page f() Chapter Skills Practice