2. Find the domain for the following functions. Write you answer in interval notation. 4

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1 Review Quiestions for Eam 4- Math 134 ( ) NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to studying all your suggested homework, quizzes, and OLHW. 1. Healthy Happy People Society just marketed GORUN tracker" that keep track of calories burned, steps taken, etc... Researchers have found that the price-demand and cost function for these GORUN trackers are as follows: p( ) 75.5, C( ) where is in thousands of trackers and C() is in thousands of dollars. (a) How many GORUN trackers will it take to maimize the revenue? (b) What is the maimum revenue? (to nearest dollar) (c) What is the break-even point(s)? (d) What would the profit be if 9000 GORUN trackers are produced and sold? (to nearest dollar) (e) What should the GORUN trackers be priced at in order to maimize the profitt? (round to nearest cent). Find the domain for the following functions. Write you answer in interval notation. 4 a. f( ) b. f ( ) c. f ( ) 3 4 d. f ( ) e. f ( ) log 5(8 6 ) f. f ( ) ln( 8) 3 g. f( ) 4 8 h. f( ) i. f ( ) The revenue and cost functions of producing units are given by C( ) Determine the following. a) Minimum break-even quantity. b) Maimum revenue. c) Maimum profit. d) Number of units to maimize profit? R( ) 64 and

2 4. Take some Deep Breaths 5. For the function f() = find: a. Degree b. Number of turning points c. End behavior d. Sketch 6. Give at least 3 different possible leading terms for the graph to the right. 7. The profit function for a hot dog vendor can be given by Determine the following. a) Maimum profit. b) Number of hot dogs necessary to maimize profit. P( ) Given f ( ) (a) y-intercept (b) -intercept(s) (c) verte (d) ais of symmetry 8. I almost forgot to put this one 9. That would be embarrassing!!! 10. Solve the following for : 7 9 (a) *9 (b) Rewrite each log equation in eponential form. (a) log b 0 (b) ln P 5 (c) log K m 1. Rewrite each eponential equation in logarithmic form. 5 (a) e J (b) H 5 a (c) y The marketing research department for a company that manufactures and sells notebook" computers established the following price-demand function: p where p is the wholesale price in dollars at which thousand computers can be sold. (round all answers to decimal places) (a) Find the Revenue function.

3 (b) Find the output that will produce the maimum revenue. (c) What is the maimum revenue? (d) What is the wholesale price per computer (to the nearest dollar) that produces the maimum revenue? 14. Find the domain for log 5(3 ) in interval notation. 15. Solve for EXACTLY (no decimals). a. ln( 14) b. 4e 16 c. 3*4 1 d. log ( 8) 5 e The supply function for a product is given by 9p 40 0 and the demand function is given by 4p68 0. What is the equilibrium price for this product? 17. The marketing research department for a company that manufactures and sells memory chips for microcomputers established the following Revenue and Cost functions: R( ) (75 3 ) C( ) 15 6 where is in millions of chips, and R() and C() are in millions of dollars. (a) Find the break even point(s). (b) What is the maimum revenue? (c) What is the Profit Function? (d) What is the maimum Profit and where does it occur? 18. How are all these people doing all this research? 19. The quantity demanded of a certain brand of DVD player is 3000/wk when the unit price is $485. For each decrease in unit price of $0 below $485, the quantity demanded increases by 50 units. The suppliers will not market any DVD players if the unit price is $300 or lower. But at a unit price of $55, they are willing to make available 500 units in the market. The supply and demand equations are known to be linear. (a) Find the demand equation. (b) Find the supply equation. (c) Find the equilibrium quantity. (d) Find the equilibrium price Find the domain for h ( ) in interval notation Solve the following for : (a) 9 7 (b) 8 4 * 5

4 . How s your Thanksgiving Break going? You are doing this over break, right? 3. Bobby and Tony decide to manufacture pillows. The fied costs for this pillow escapade is $4,000. It will cost them $10 to produce each pillow, but they plan to sell them at $30 each. (a) If they manufacture and sell eactly 37 pillows, how much of a profit/loss could they epect? (b) How many pillows must Bobby and Tony sell in order to break even? 4 4. Find the domain for h ( ) in interval notation Wow, you sure are lucky that your teacher does these big reviews! 6. For the function f( ) find: 5 a. -intercept(s) b. y-intercept c. vertical asymptote(s) d. horizontal asymptotes e. sketch 7. Solve for : 4 log 4(3 1) 7 8. Let p( ) and C( ) 9000 be the price-demand equation and the cost function, respectively for the manufacturing of umbrellas. (a) What is the Revenue Function? (b) What are the break even point(s)? (c) What is the Profit Function? (d) What is the maimum Profit? (e) How many umbrellas are needed to maimize the Profit? (f) What should the umbrellas be priced at to reach the maimum Profit? 9. Solve 3 17() Given f ( ) find (a) y-intercept (b) -intercept(s) (c) verte (d) ais of symmetry 31. Find the domain of: (a) g( ) 3. Solve + 5 e (b) h ( )

5 33. Solve ln(5) = y 34. For the function to the right, a. How many turning points?. b. Is the degree odd/even? c. What is the smallest possible degree? d. Is the leading coefficient positive or negative? e. What is a possible leading term? Solve Give at least 3 different possible leading terms for the graph to the right. 37. In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost, C(), in dollars to produce items. They estimate the cost to produce 10,000 items as $547,500, and the cost to produce 50,000 items as $737,500. (a) Find a formula for C(). (b) Find the total cost to produce 100,000 items. (c) How many items are produced if the total costs are $50,89.50? (d) Find the marginal cost of the items to be produced in this plant and what does it mean to the manager? 38. Find the domain of ln(4 9) in interval notation. 39. Find the equation of the line going through the points (350,90) and (410,770). 40. The price-demand function and cost function for a certain product are given below p( ) C( ) where is in thousands of units, p() is in dollars, and C() is in thousands of dollars. (a) What is the maimum revenue? (to nearest dollar) (b) At what price will the Revenue be maimized? (c) What is the break-even point(s)? (d) How many units does it take to maimize the profit? (e) What is the profit when 15,000 units are produced/sold? 41. The quantity demanded for a certain brand of washing machine is given by 3 p and supply equation for the washing machine is given by p 400, 3 3 where is the quantity demanded and p is the price. What is the equilibrium price for the washing machine?

6 4. Solve Fred and George produce and sell Wacky Wands. They discovered the pricedemand equation to be (p) where p() is the price of the wands (in dollars) and is the number of wands. The cost equations for wacky wands is given by C() = , where C() is the cost of the wands (in dollars) and is the number of wands. (a) How many wands must they sell in order to maimize the revenue? (b) How many wands must Fred & George produce & sell to break even? (c) What is the maimum profit they could make on these wands? (d) What should the price of the wands be in order for them to maimize profit? 44. Give at least 3 different possible leading terms for the graph to the right. 45. For the function f ( ) find: 8 a. -intercept(s) b. y-intercept c. vertical asymptote(s) d. horizontal asymptotes e. sketch Find the domain of f () in interval notation Solve ( e ) e A company markets potato launchers. They have discovered that the demand for these launchers is given by (p) The cost function for the company is given by C( ) Hint: -ma=1500, y-ma=00,000 (a) What is the revenue function? (simplify) (b) How many potato launchers would it take for the company to break-even? (round to nearest whole number) (c) What should the potato launchers be priced at in order to maimize revenue? (round to nearest dollar) (d) Find the profit equation (and simplify). (e) What is the maimum profit? (round to nearest cent...aka decimal places)

7 49. For the function f ( ) 7 9 find: a. Degree b. Number of turning points c. End behavior d. Sketch 50. Solve log 4(5 1) 51. Given f ( ) , find (a) y-intercept (b) -intercept(s) (c) verte (d) ais of symmetry 5. For the function f() = find: a. Degree b. Number of turning points c. End behavior d. Sketch 53. Almost done! 54. Suppose that the demand and price for strawberries are related by: p D( q) 5 0.5q where p is the price (in dollars) and q is the quantity demanded (in hundreds of quarts). (a) Find the price when the demand level is 840 quarts. (b) Find the quantity demanded for the strawberries when the price is $.40. Suppose the price and supply of strawberries are related by p = S(q) = 0:5q where p is the price (in dollars) and q is the quantity demanded (in hundreds of quarts) of strawberries. (c) Find the quantity supplied at a price of $. (d) What is the equilibrium quantity for the strawberries? (e) What is the equilibrium price for the strawberries? 55. Give at least 3 different possible leading terms for the graph to the right For the function f ( ) find: 1 a. -intercept(s)

8 b. y-intercept c. vertical asymptote(s) d. horizontal asymptotes e. sketch 57. Last test of the semester! 58. Solve without a calculator. Write answers EXACTLY (no decimals). 8 3 (a) (b) 64 (c) Dr. Poage has decided to produce and sell rings that say 1 MATH!" The pricedemand equation and cost function for the production of these rings are given respectively by: p 00 C( ) where is the number of rings that can be sold at a price of $p per ring and C() is the total cost (in dollars) of producing rings. (a) Determine the break even point(s). (b) What is the maimum Revenue and how many rings are needed to maimize the Revenue? (c) What should the rings be priced at in order to maimize the Revenue? (d) How many rings are needed to maimize the Profit and what is the maimum profit? (e) What should the rings be priced at in order to maimize the profit?

1324 Exam 4 Review. C(x) = x

1324 Exam 4 Review. C(x) = x c Dr. Patrice Poage and Mrs. Reanna Carr, June 26, 2015 1 1324 Exam 4 Review NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to studying