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F.IF.6 [578946]StudentClassDate

1. What is the average rate of change for the function over the interval

A.

B.

C.

D.

2. What is the approximate average rate of change of the function over the interval of to

A. 0.8

B. 1.2

C. 2.1

D. 3.7

3. Fredrick recorded the temperature on five separate days during

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the month of July. The data is shown in the table below.

Date in July Temperature 1 89°F 6 93°F

10 91°F 18 95°F 29 °F

Between which two dates did the temperature increase at the fastest rate?

A. 1 and 6

B. 6 and 10

C. 10 and 18

D. 18 and 29

4. Over which interval do the functions and have the same average rate of change?

A.

B.

C.

D.

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5. The table below shows the number of minutes Leo played basketball and the total number of calories he burned.

Time (minutes)

Total Calories Burned

15 10025 11640 25050 35070 500

What is the approximateaverage rate of change in the total calories Leo burned between 40 and 70 minutes?

A. 7.71

B. 8.21

C. 8.33

D. 8.75

6. A function, f(x), is graphed on the coordinate plane below.

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What is the interval of x values over which the rate of change of the function is zero? Respond by using the format (a, b), where a and b are the appropriate x values that identify the interval.

7. A toy rocket is launched from the roof of a building. The graph below shows the height of the rocket x seconds after it was launched. What is the average rate of change of the height of the rocket during its descent?

A. ft/sec

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B. ft/sec

C.ft/sec

D. ft/sec

8. The table below shows the cost to rent a movie for different numbers of days at a movie rental store.

Days Total Cost 3 $6.00 5 $8.50 6 $9.75 9 $13.50

What is the meaning of the rate of change for the data?

A. The cost to rent a movie increases by $1.25 for each additional day the movie is rented.

B. The cost to rent a movie increases by $2.00 for each additional day the movie is rented.

C. The cost to rent a movie increases by $2.50 for each additional day the movie is rented.

D. The cost to rent a movie increases by $2.75 for each additional day the movie is rented.

9. Which of these expressions represents the average rate of change of the

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function over the interval from x to

A.

B.

C.

D.

10. The table below shows the amount of time Tyler studied before 4 math tests, and the grade he earned on each test.

Minutes Studied (x)

Test Grade (y)

0 80 5 81

20 84 60 92

Which statement correctly describes the average rate of change?

A. Tyler’s test grades improved 1 point for every 2 minutes he studied.

B. Tyler’s test grades improved 1 point for every 5 minutes he studied.

C. Tyler’s test grades improved 2 points for every 1 minute he

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studied.

D. Tyler’s test grades improved 5 points for every 1 minute he studied.

11. A projectile travels straight up from a height of 5 feet with an initial velocity of 80 feet per second. The height (y) in feet of the projectile as a function of time (t) in seconds can be modeled by

Part A: What is the average rate of change on the interval [1, 2]? Show your work.

Part B: Determine an interval such that the average rate of change is negative.

12. What is the approximate average rate of change for f(x) = 15(1.5)x from x = 2 to x = 5?

A. 16

B. 23

C. 27

D. 69

13. A volleyball camp charges $150 per camper for 10 campers. When a team brings 15 campers, the rate is reduced to $125 per camper. What is the rate of change in cost per camper?

A. $2.50

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B. $5.00

C. $8.34

D. $10.00

14. Using the table of selected values of below, calculate the average rate of change of over the interval

01 2 3 4 5

79 12

16

14

12

A.

B.

C.

D.

15.For the function what is the average rate of change over any given interval?

A.

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B.

C.

D.

16. The table below records the median salary at United Construction over a period of 4 years.

Year Salary

2009 $35,0002010 $36,0002011 $38,0002012 $40,0002013 $43,000

What is the average annual increase in the median salary from 2009 to 2013?

A. $2,000

B. $8,000

C. $38,000

D. $38,400

17. The table below shows the number of people that visited a state park over a period of 4 days.

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Day Number of People (thousands)

1 5 2 9 3 13 4 17

What is the meaning of the rate of change for the data?

A. The park had an decrease in attendance of 4,000 people per day.

B. The park had an decrease in attendance of 4 people per day.

C. The park had a increase in attendance of 4,000 people per day.

D. The park had a increase in attendance of 4 people per day.

18. What is the average rate of change of the function f(x) = 2x2 + 4 over the interval [–4, –1]?

A. –3

B. –4

C. –6

D. –10

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19. The average rate of change of is 2 on the interval from to Which of these could describe the values of when and

A.

B.

C.

D.

20. The table below shows the total number of computer parts Donavon can assemble during a 4-hour work shift.

Hours Worked Parts Assembled 0 0 1 512 2 1,024 3 1,490 4 1,972

What is Donavon’s average number of parts per hour for his entire 4-hour shift?

A. 493 parts per hour

B. 512 parts per hour

C. 657 parts per hour

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D. 1,972 parts per hour

21. The table below shows the number of hours a gas station was open and the number of gallons of gas sold.

Hours Opened

Gallons of Gas Sold

1 3683 1,0096 2,6648 3,445

What is the average rate of change in the amount of gas sold between hours 3 and hours 8?

A. 390.5 gallons per hour

B. 439.6 gallons per hour

C. 487.2 gallons per hour

D. 890.8 gallons per hour

22. During a recent snowstorm, John measured the total snowfall accumulated at the end of each hour. He recorded his results in the table below.

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What is the approximate average rate of change of the snowfall between 1 p.m. and 6 p.m.?

A. 0.7 inch/hour

B. 0.9 inch/hour

C. 1.1 inches/hour

D. 1.4 inches/hour

23. The table below shows the values of function for different values of x over the interval What is the average rate of change of the function over the interval

24. The table below shows the height of a pyramid-shaped candle as it burns.

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Time (min.) Height (in.)0 62 55 413 3 45 2109 1

What would be the average rate of change of the candle's height from the time it is lit until 45 minutes has passed? Show your work or explain your answer.

25. The population of one variety of frogs in a nature preserve is listed in the table below.

Year Population 1990 1,750 1995 1,900 2000 1,950 2005 2,180 2010 2,240

What was the average rate of change in the population between 1990 and 2000?

A. 20 frogs per year

B. 24.5 frogs per year

C. 28.7 frogs per year

D. 30 frogs per year

26. The function f(x) = 125(0.80)x models the retail price of a CD player x years since it was first produced. What is the average

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rate of change in the retail price between years 2 and 4?

A. $28.80 per year

B. $14.40 per year

C. –$28.80 per year

D. –$14.40 per year

27. Which expression is equivalent to the average rate of change of the function f(x) over the interval [4, 9]?

A.

B.

C.

D.

28. A function is shown in the table below.

x f(x) 0 1,750 3 1,900 7 1,950 9 2,180

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11 2,240

During which interval was the average rate of change the greatest?

A. 0 to 3

B. 3 to 7

C. 7 to 9

D. 9 to 11

29. The table below shows the number of miles Paul ran over five days.

Day Miles Ran1 1.52 0.753 2.54 1.255 2.5

What is the approximate average rate of change in the number of miles Paul ran from day 2 to day 5?

A. 0.4

B. 0.6

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C. 1.7

D. 1.8

30. Sam and Jason run the two-mile race for the school track team. The table below shows their times for the first 4 races.

Race Sam Jason 1 17.6 minutes 18.5 minutes 2 16.5 minutes 17.3 minutes 3 16.3 minutes 16.2 minutes 4 15.2 minutes 15.8 minutes

What is the difference between Jason’s average rate of change and Sam’s average rate of change from race 1 to race 4?

A. 0.9 minutes

B. 0.6 minutes

C. 0.4 minutes

D. 0.1 minutes

31. The graph shows the distance Mila drove during the first 10 minutes of her drive to work one morning.

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What was Mila’s average speed, in miles per hour (mph), during the first 5 minutes of her drive?Use words, numbers, and/or pictures to show your work.

32. What is the average rate of change for the function f(x) = 4(0.5)x over the interval –1 ≤ x ≤ 2?

A.

B.

C.

D.

33. The population of a small town from the year 2000 to 2005 is represented by the function,

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with x representing the number of years since 2000. Which statement is true about ?

A. The average yearly population growth rate is 5%.

B. The average yearly population growth rate is 105%.

C. The annual population increases by 750 people.

D. The annual population increases by 15,750 people.

34. What is the average rate of change of over the interval

A.

B.

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C.

D.

35. The graph of a function is shown below.

What is the average rate of change over the domain

A. -3

B. -2

C. 2

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D. 3

36. The average rate of change of the function represented by the table below between and is

What is the value of a?

A.

B.

C.

D.

37. The graph below shows a distance versus time graph. What is the average speed between 2 p.m. and 4 p.m.?

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A. 25 miles per hour

B. 62.5 miles per hour

C. 75 miles per hour

D. 137.5 miles per hour

38. A biologist estimated that the population of bacteria in a medium after t hours can be modeled by the expression where I represents the initial population at time Which of these represents the ratio of the average rate of change of the population in the first two hours to the average rate of change of the population over the next two hours (between time and )?

A.

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B.

C.

D.

39. The graph shows the number of bacteria present in an experiment.

What is the rate of change for the number of bacteria from to

A. 1,000 bacteria per hour

B. 2,000 bacteria per hour

C. 3,000 bacteria per hour

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D. 4,000 bacteria per hour

40. Dwight is a right-handed archer. When he holds his left hand out to the side, his maximum draw length is the distance from the middle of his left palm to his right shoulder. For the last five years, Dwight has been interested in the relationship between his height and maximum draw length. Each year on his birthday, he added to the following table.

Based on the data, between the ages of 12 and 14, what was the average rate that Dwight's draw length changed per cm of height growth?

41.

What is the average rate of change of the function over the interval

A.

B.

C.

D.

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Age 12 13 14 15

Height (cm) 157

160

167

169

Draw Length (cm) 96 100

101

109

42. What is the average rate of change of the function graphed below over the interval

43. The table below shows the distance Russell rolled a ball after different amounts of time.

Time (seconds)

Distance (feet)

1 4.5 2 6 3 8.5 4 12 5 16.5

What is the average rate of change in the distance Russell rolled the ball between 1 and 5 seconds?

A. 2.4 feet per second

B. 3.0 feet per second

C. 3.3 feet per second

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D. 4.0 feet per second

44. An exponential function is shown in the table below.

x f(x)1 123 1085 9726 2,916

What is the average rate of change of the function over the interval x = 0 to x = 4?

A. 48

B. 80

C. 81

D. 240

45. Jamie bought a new video game. The table below shows her score after playing the game different numbers of times.

Times Played Score 1 10,865 2 11,189 3 11,513 4 11,837

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5 12,161 6 12,485

What was Jamie’s average rate of change between game 3 and game 6?

A. 162 points per game

B. 270 points per game

C. 324 points per game

D. 972 points per game

46. What is the average rate of change of the function below over the interval of to

A.

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B.

C.

D.

47. In 2007, Zack bought a new car for $17,500. The table below shows the value of the car between 2007 and 2012.

Part A. Calculate the average rate of change of the value of the car between 2007 and 2008. Explain what your answer means in terms of the car’s value over this interval.

Part B. Calculate the average rate of change of the value of the car between 2008 and 2012. Explain what your answer means in terms of the car’s value over this interval.

Part C. Compare the values from Part A and Part B. What can you conclude based on this comparison along with the data in the table in terms of the car’s value over the time period shown in the table?

Use words, numbers and/or pictures to show your work.

48. The population growth for a species of birds, in thousands, can be

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represented by the function where t is the number of years since 2002. What is the approximate average rate of change of the population between the years of 2004 and 2007?

A. 9.3 thousand birds/year

B. 14.3 thousand birds/year

C. 27.9 thousand birds/year

D. 42.9 thousand birds/year

49. The graph below shows the total number of fish that a fisherman caught over a 5-week time period.

What was the average rate of change in the number of fish

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caught per week between weeks 2 and 5?

A. about 13 fish per week

B. about 18 fish per week

C. about 32 fish per week

D. about 40 fish per week

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