Exam 1 Review Name: e. Write an expression that represents the number of rolls of wrapping paper needed to cover 34 square feet of surface.

Transcription

1 1. Suppose that a roll of wrapping paper covers 100 square feet of surfaces. Also, a roll of wrapping paper costs $2.50 per roll plus a $2 processing fee per order. Assume that you can purchase fractional rolls of wrapping paper. a. Identify two quantities that are related by a constant rate of change. What is this constant rate of change and what does it mean in the context of this problem? b. A function f determines the number of rolls of wrapping paper needed, w, as a function of the number of square feet of surfaces you want to cover, A. i. What is the input quantity of function f? ii. What is the output quantity of function f? iii. Define function f. c. A function m determines the cost of wrapping paper (in dollars), c, as a function of the number of rolls of wrapping paper needed, w. i. What is the input quantity of function m? ii. What is the output quantity of function m? iii. Define function m. e. Write an expression that represents the number of rolls of wrapping paper needed to cover 34 square feet of surface. f. Write an expression that represents the cost of wrapping paper (in dollars) to buy 3 rolls of wrapping paper. g. Write an expression that represents the cost of wrapping paper (in dollars) needed to cover 125 square feet of surface. 2. Given g(x) = 3x + 6 and m(x) = 2x 4, find the value of x where g(x) = m(x)

2 3. Given y = f (x) and f (x) = 2x 2 3, find f Given h(x) = x 3 x + 10 and g(x) = 2x + 2, find h(g(x)) and h(g(1)). 5. A linear relationship exists between the quantities whose values are represented by x and y. What is the value of y when x is 4? Write an equation that relates x and y. x y (Use the following statement to answer questions 6-8) Paulo is running along the beach at a constant rate of 3 ft/sec. 6. How many feet does Paulo travel in 11.8 sec? 7. How many seconds (rounded to the nearest hundredth) will it take for Paulo to travel 132 feet? 8. Write a formula that determines Paulo s distance d from a milepost (in feet), given the amount of time t (in seconds) since Paulo passed the milepost? (Use the following information to answer questions 9-10) On a sunny winter day in Illinois, a spherical snowball has a radius of 10 cm and as it melts, the radius decreases at a rate of 0.4 cm/minute. Recall that the volume of a sphere is determined by V = 4 3 πr What is the volume of the snowball 5.3 minutes after it begins melting? 10. Write a function g to define the volume of the snowball (in cm 3 ) as a function of the amount of time (in minutes) since the snowball began melting?

3 11. The height of a boomerang thrown in the air can be modeled by the function h = f (t) =.63t t + 5 where h is the height of the boomerang (in feet) above the ground t seconds after being thrown. What is the average speed of the boomerang as it travels during the time interval from 2 second to 3 seconds after it was thrown? Write a statement that describes the meaning of average speed in this context. 12. Suppose the function g represents the cost of tuition at ASU t years since What does the expression 3 g(6) represent? Use the tables below to answer questions 13 & 14 x f(x) x g(x) Determine a. b. g(f(-2)) c. 14. If, what is the value for x? (Use the following information to answer questions 15-16) Nathan is running a marathon. Let d be the distance in miles of Nathan from the starting line, and let t be the number of minutes since she began running. The distance d is a function of the time t and is represented by the function f, defined d = f(t) = 3.2t 2 + 3t. 15. What is the meaning of f(7) f(3)? 16. Suppose you determine the average speed of Nathan over the interval t = 1 to t = 4 sec. Write an expression using function notation to represent the average speed of Nathan over this interval then write a statement that best describes the meaning of average speed in this context? 17. What is the domain of the function n, given that n(x) = x 3 x 10? 18. A bucket is filled with water up to the 7 gallon mark. The bucket springs a leak and water begins draining at a constant rate of 3/8 gallon per minute. Write a formula to determine the number of gallons of water n in the bucket in terms of the number of minutes t the water has been draining.

4 19. A large spool is used to hold rope, which is wound around the spool. The more rope wound around the spool, the greater the combined weight of the spool and rope. The graph below shows that when 5 feet of rope is wound around the spool, the total weight of the spool and rope is 3.95 pounds. The rope weighs 0.19 pounds per foot. Total weight of spool and rope (in pounds) (5, 3.95) Write a formula that determines the total weight of the spool and rope t in terms of the number of feet n of rope that is on the spool Total length of rope on the spool (in feet) 20. Lisa and Sarah decided to meet at a park bench near both of their homes. Lisa lives 2390 feet due west of the park bench and Sarah lives 1420 feet due east of the park bench. Sarah left her house at 7:00 pm and traveled at a constant speed of 210 feet per minute towards the bench. Lisa left her house at the same time traveling a constant speed of 330 feet per minute towards the bench. Define a formula that relates the distance between Lisa and Sarah in terms of the number of minutes since 7:00pm. Use the following graphs of g and r to answer questions Use the graph of g to solve g(x) = 5 for x. 22. Evaluate r(g(4.5)) 23. Evaluate g(r( 2)) 24. Evaluate g 1 (r( 2)) 25. Evaluate r 1 (r(3)) 26. Find the value of h(3) when p( x) = 3x +10 and h( x) = 3p( x) Joe is 234 months old and Alex is 356 months old. How many times as old is Alex as Joe?

5 Use the following information for questions 28 and 29. An 8 ft x 4 ft piece of plywood is being used to build an open-top toy chest. The chest is formed by making equal-sized square cutouts from two corners of the plywood at the ends of an 8-foot side. After these squares are discarded, three more cuts are made (at the dashed lines on figure) and these pieces are folded up and secured to create three of the four vertical sides. When the open side is placed against a wall, the open top toy chest is formed. Neglect the thickness of the wood when answering these questions. 28. If the variable x represents the length of a side of the square cutouts in feet, what are the possible values of x in this context? 29. Define a function, f, that gives the volume of the toy chest (in cubic feet) in terms of the length of a side of the square cutout (in feet). 30. Jenessa is taking a vacation to London, UK and Paris, France. Jenessa will need to convert her US dollars to UK pounds while in London and to Euros while in Paris. The function f determines the number of UK pounds in terms of the number of US dollars, n u. The function h determines the number of Euros in terms of the number of UK pounds, n k. Using the current conversion rates the functions f and h are defined by: f (n u ) = 0.77n u and h(n k ) = 1.17n k Define a function g that Jenessa can use to determine the number of Euros g(n u ) she will receive for n u US dollars.