Math 112 Spring 2018 Midterm 1 Review Problems Page 1

Transcription

1 Math Spring 8 Midterm Review Problems Page Note: Certain eam questions have been more challenging for students. Questions marked (***) are similar to those challenging eam questions.. Which one of the following points lies on the graph of the function f ( ) 5?, 5,, 5,. Determine the domain of,,,,, (E), g. 5. Determine the domain of h 7., 7, 7,, 7 (E), 7. Given f 7, evaluate a f. f a a 7a 8 f a a 9a f a a a 6 f a a 9a 8 (E) None of these

2 Math Spring 8 Midterm Review Problems Page Questions 5 and 6 refer to the following situation: The braking distance, in feet, of a car traveling v at v miles per hour is given by dv.v. 5. Evaluate d and give a practical interpretation. d d d d. A car traveling miles per hour will require a braking distance of feet.. A car traveling miles per hour will require a braking distance of feet.. A car traveling feet will require a braking distance of feet.. A car traveling feet will require a braking distance of feet. 6. Suppose that the car took 5 feet to brake. Approimately how fast was the car traveling? The speed that the car was traveling was: Less than 75 miles per hour Between 75 and 77 miles per hour Between 77 and 79 miles per hour Between 79 and 8 miles per hour (E) More than 8 miles per hour f t. 7. Given f r r r, evaluate t t 7 t t t 7 t t 5 (E) t 8. For f 9, find and simplify f ( h) f ( ). h h h 8 9h 8 h h h 8 8 h h 9 h (E) 9

3 Math Spring 8 Midterm Review Problems Page Questions 9 and refer to the following situation: The Karmen line, or the line between the earth s atmosphere and space, is approimately, meters above sea level. A spacecraft, launched from sea level, height in meters above ground, is given by ht 9.8t 88t, where t is measured in seconds. 9. Evaluate h 5 and give a practical interpretation. h 5 87,. After 5 seconds, the spacecraft will be traveling at a speed of 87,65 meters per second. h 5 87,. Traveling at a speed of 5 meters per second, the spacecraft will be at an altitude of 87,65 meters. h 5 87,. After 87,65 seconds, the spacecraft will be 5 meters from the Karmen line. h 5 87,. The spacecraft, after 5 seconds, will have reached a height of 87,65 meters When, in seconds, does the spacecraft reach the Karmen line of, m? The spacecraft reaches the Karmen line in: Less than seconds Between and 5 seconds Between 5 and 5 seconds Between 5 and 55 seconds (E) More than 55 seconds

4 Math Spring 8 Midterm Review Problems Page. Which one of the following graphs DOES NOT represent a function?

5 Math Spring 8 Midterm Review Problems Page 5. (***) Solve each of the following equations for y and graph the formula(s) on your graphing calculator. Which one of these equations represents y as a function of? y y 5y 5 y (E) y 7. (***) A company has marketing analysts and asks each person to make predictions for products that will be sold. Which one of the tables below represents y as a function of? (E) Year () Sales (y) 9 Year () Color (y) Blue Green Blue Red Sales () 9 Price (y) $ $85 $6 $ Price () $5 $ $ $5 Sales (y) 5 7 Year () Price (y) $8 $6 $7 $5

6 Math Spring 8 Midterm Review Problems Page 6 The following graph depicts the number of commercial banks in Arizona as a function of the year, over a several year period. Use this graph to answer questions and 5. (Please ignore the gray shading on the graph.). Identify the domain and range of this function. Domain: [, ] Range: [9, 5] Domain: [, ] Range: [9, 55] Domain: [9, 5] Range: [, ] Domain: [9, 55] Range: [, ] (E) Domain: [, ] Range: [5, 55] 5. Identify the interval(s) over which the number of commercial banks was decreasing during this period. (9, 55) (5, 55) (8, ) (, 8)

7 Math Spring 8 Midterm Review Problems Page 7 The following graph depicts the population of Ukraine, in millions, as a function of the year, over a several year period. Use this graph to answer questions 6 and 7. (Please ignore the gray shading on the graph.) 6. Identify the domain and range of this function. Domain: [97, 5] Range: [5M, 5.M] Domain: [97, 5] Range: [5M, 5M] Domain: [7M, 5.M] Range: [97, 5] Domain: [5M, 5M] Range: [97, 5] (E) Domain: [97, 5] Range: [7M, 5.M] 7. Identify the interval(s) over which the population of Ukraine was decreasing during this period. (5M, 5.M) (7M, 5.M) (99, 5) (97, 99)

8 Math Spring 8 Midterm Review Problems Page 8 8. (***) The top 5 hottest temperatures recorded in Tucson until the year are shown in the table below [Source: National Weather Service]. Temperatures are given in degrees Fahrenheit. Temperature Date 7 degrees 6/6/9 6 degrees 6/9/9 5 degrees 6/8/9 5 degrees 6/5/9 degrees 7/8/95 degrees 7//89 degrees 6//88 degrees 6/7/95 degrees 6/6/9 degrees 6//9 degrees 6/6/9 degrees 6/8/9 degrees 6/5/9 degrees 6/8/89 degrees 6//88 Which one of the following statements is true about this data? The date is a function of the temperature. The temperature is a function of the date. Neither of the above statements is true.

9 Math Spring 8 Midterm Review Problems Page 9 9. (***) The average normal rainfall for Tucson, by month, over the time period of 98- is shown in the table below [Source: National Weather Service]. Rainfall vales are given in inches. Month Rainfall Normal January.9 February.86 March.7 April. May. June. July.5 August.9 September.9 October.89 November.57 December.9 Which one of the following statements is true about this data? Normal rainfall is a function of the month. Month is a function of the normal rainfall. Neither of the above statements is true.. A new car salesperson is paid a monthly salary of $5 plus a commission of 5% of all the sales she makes each month. What monthly sales amount would give her of a monthly income of $,? $5 $, $,5 $, (E) $,

10 Math Spring 8 Midterm Review Problems Page. (***) An item is originally priced at P dollars, but is placed on sale at a discount of 5% off. If the sales ta is %, which of these epresses the final sales price, F, as a function of P? F( P).. 5P.P F( P).75.75P F( P)..P F( P) (E) F( P).. 75P.5 y g. The graph of is shown below. Use the graph to find the domain and range of g g Domain: (, ) Range: [, ) Domain: [., ) Range: [, ) Domain: [, ) Range: [., ) Domain: [., ) Range: [., ) (E) Domain: [, ) Range: (, ) - -

11 Math Spring 8 Midterm Review Problems Page. Which one of the following has a domain of all real numbers ecept? y y y 6 y (E) 8 y y. The graph of f is shown below. Use the graph to determine the value of 6 f f (E) 5

12 Math Spring 8 Midterm Review Problems Page y T 5. (***) Identify the open interval(s) where the graph of is decreasing , and, only, 6 only, only, and, (E), only only 6. (***) Identify the open interval(s) where the graph of T y is positive., only, and, 6 only, only, and, (E), and, only only

13 Math Spring 8 Midterm Review Problems Page 7. Determine the -intercept(s) of r. 5, (E), only,,, and, and,,, only and only,, only only 8. Determine the intercepts of the function graphed below (E), and, only, and, only,,,, and,,,,, and,, and, only only only

14 Math Spring 8 Midterm Review Problems Page Questions 9, and, refer to the following situation: A manufacturer of DVD players estimates that the profit for producing and selling players is given by the function P 58 8, 5. Graph this function in your calculator (***) Find the -intercepts on the graph of this function, and give a practical interpretation. 5, The -intercepts are,,75,, and 8,5,. The manufacturer would make $ in profit by selling 5 DVD players,,75 DVD players, and 8,5 DVD players. 5, The -intercepts are,,75,, and 8,5,. The manufacturer could sell a minimum of 8,5 DVD players, a maimum of,75 DVD players, or 5 DVD players. and,75,. The manufacturer would make $ in profit by selling 5 DVD players and,75 DVD players. 5, The -intercepts are The -intercepts are 5, and,75,. The manufacturer could sell a minimum of 5 DVD players and a maimum of,75 DVD players.. On what interval(s) is the profit function increasing? 5, 65, 65 5,,75,,75 (E), 5,8. According to this model, what is the maimum profit? The maimum profit is: More than $9, Between $85, and $9, Between $8, and $85, Between $75, and $8, (E) Less than $75,

15 Math Spring 8 Midterm Review Problems Page 5 g.. Determine the intercepts of,,, and, and, and, only only only, and, only (E) None of these. Write the equation of the linear function with slope of,., that passes through the point y y y y (E) y 5.. Write the equation of the linear function passing through the points, and, 5 y y 6 9 y 5 y 6 9 (E) y Write the equation of the linear function through the point, 5 and having a slope of. 5 y 5 (E) y

16 Math Spring 8 Midterm Review Problems Page 6 6. Which of these lines has a slope of zero? y. 5 y 5 A By C, where A is positive, B is negative, and C is a real number y 5 7. Determine an equation for the linear function graphed below y y y y (E) y 8. The rental fee for a compact car is $8 per day (Monday through Thursday) and $ per day (Friday through Sunday). This rental fee includes free miles per day. Additional miles cost $.5 per mile. Write an equation for the total cost of a rental, c, from Wednesday through Saturday ( complete days) where represents the number of miles traveled and is greater than. (You may ignore the ta). c 8.5 c 8.5 c 8.5 c 8.5

17 Math Spring 8 Midterm Review Problems Page 7 A couple invests $5 to build a rose garden. On the average, it costs them $.5 to grow each rose and each rose can be sold for $.75. Use this information to answer questions 9 and. 9. Create a formula for a cost function and a revenue function. Let be the number of roses sold. C 75 R 5. and. C.75 5 and R. 5 C.5 5 and R. 75 C. 5 and R. 75 (E) C 5 and R.. How many roses must the couple sell to break even?,,5, 8,5 (E) None of these A company invests $78,75 in the production of iphone cases. On the average, it costs them $7.5 to make each case and each case can be sold for $.5. Use this information to answer questions and.. Create a formula for a cost function and a revenue function. Let be the number of cases sold. C 7. 5 and R. 5 C , 75 and R. 5 C.5 78, 75 and R 7. 5 C. 5 and R 7. 5 (E) C 78, 75 and R. How many cases must the company sell to break even?,75,5 6,5 7,5 (E) None of these

18 Math Spring 8 Midterm Review Problems Page 8 The following table shows test market data shows the relationship between the purchase price and the demand for a new product (the number of units that people are will to purchase). Purchase price, p, (in dollars) 5 Number of units, q, 75, 6,5 5, Use this data to answer questions and.. (***) Epress the price as a function of the number of units. 5 q 5 q 5 q p 5 p, 5 p 5, p q q 5 p q p q 5 (E) q p. Using the function found in the previous question, find the slope of the linear function, and give a practical interpretation. The slope is. For every one unit increase, the price decreases by $5. 5 The slope is. For every $ price increase, the number of units decreases by 5. 5 The slope is. For every $ price increase, the number of units increases by 5. 5 The slope is 5. For every one unit increase, the price decreases by $5. (E) The slope is 5. For every $ price increase, the number of units decreases by 5.

19 Math Spring 8 Midterm Review Problems Page 9 Questions 5, 6 and 7, refer to the following situation: A network is tracking the viewership of a new television show. After 5 weeks on the air, the number of viewers was 8,,. After another 5 weeks, the number of viewers had dropped to 6,,. Assume that the viewership has been decreasing linearly. 5. Write a function to model the number of viewers as a function of the number of weeks the show has been on the air. N w, w N w,w 8,, N w, w,, N w,w 6,, (E) N w,w,, 6. What is the slope of this function, and what does it tell you in practical terms? The slope is,. After 5 weeks, there are, fewer people watching the television show. The slope is,. Each week, there are, fewer people watching the television show. The slope is,. There are, people who started watching the television show. The slope is,. Eventually, only, people watching the television show. (E) The slope is,. Each week, there are, more people watching the television show. 7. According to this model, how many viewers watched the show initially?,,, 6,, 8,, (E),,

20 Math Spring 8 Midterm Review Problems Page Questions 8, 9 and 5, refer to the following situation: Vehicles commonly depreciate in value as they grow older. Samantha purchases a new car. After year, the value of the car has depreciated to $,5. After years, the value of the car has depreciated to $8,. Assume that the car s value has been decreasing linearly. 8. Write a function to model the depreciation of the car as a function of years since the initial purchase where D t it the value of the car, t years after purchase. D t 5 t D t 5t 5, D t 5 t, 5 D t 5t 8, (E) D t 5t 79, 5 9. What is the slope of this function, and what does it tell you in practical terms? The slope is, 5. Each year, the car decreases in value by $,5 The slope is, 5. Every two years, the car decreases in value by $,5 The slope is, 5. Within one day of purchase, the car decreases in value by $,5 The slope is, 5. Eventually, the car s value will only be $,5 (E) The slope is, 5. Each year, the car increases in value by $,5 5. According to this model, what was the initial purchase price of Samantha s car? $8, $,5 $5, $79,5 (E) Cannot be determined from information provided

21 Math Spring 8 Midterm Review Problems Page 5. The typical costs for two different kinds of heating systems for a bedroom housing unit are given in the table below: Type of System Installation Cost Operation Cost/Year Electric $5, $, Solar $, $5 After how many years of operation will the total costs of solar heating and electric heating be the same? Less than 5 years Between 5 and years Between and 5 years Between 5 and years (E) More than years 5. A concert venue holds a maimum of people. With ticket prices at $5, the average attendance is 6 people. For every $5 the ticket price is lowered, approimately 5 more people attend. Which of the following represents the number of people attending as a function of price? N p 5p 6 N p 5p 85 N p 5p 5 N p p 5 p 5 85 (E) N p 5 5. Evaluate g given that: g 5 for for and (E) None of these

22 Math Spring 8 Midterm Review Problems Page 5. Which one of the following is the graph of the function if f? if

23 Math Spring 8 Midterm Review Problems Page 55. Determine the range of the function given by 5 g (,] ], ( (,) (,) (E) ), ( 56. Determine the rule that defines the piecewise-defined function graphed below. 5 if if f 5 if if f 5 if if f 5 if if f

24 Math Spring 8 Midterm Review Problems Page 57. Nell has a sales clerk job that pays $ per hour for regular work hours (less than or equal to hours per week). She gets double time (or $ per hour) for any hours over that she works in a week. Which of the following functions can be used to represent Nell s weekly pay for working h hours in a week? h P h P h h h h h h h h 8 h P h P h h h h 8 h h (E) P h h h h Questions 58 and 59 refer to the following situation: An online novelty shop sells cheap fidget spinners in bulk. They charge $.5 each for the first 5 spinners, and $.75 each for any additional spinners. 58. Which of the following functions represents the total cost of an order of fidget spinners as a function of the number of spinners purchased?.5.75 if 5 C C if if if if 5 C C if if if 5 5 (E) C if if Dakota places an order of fidget spinners and gets a bill for $5. How many spinners did Dakota buy? The number of fidget spinners that Dakota bought was: Less than 5 Between 5 and 5 Between 5 and 5 Between 5 and 55 (E) More than 55

25 Math Spring 8 Midterm Review Problems Page 5 Questions 6 and 6 refer to the following situation: The Arizona 6 ta brackets are such that, single ta payers making between $ and $, income, are required to pay a flat Arizona.59% ta rate. For single ta payers making greater than $, income but less than or equal to $5, income, they must first pay.59% ta on the first $, and then.88% of any remaining income greater than $, (for an income of $5,, this would be.88% of the $5, greater than $, and.59% of the first $,). 6. Which of the following functions represents the Arizona 6 ta bracket for single ta payers? T if, if, 5, T if, if, 5, T.59.88( ) if, if, 5, T ( ) if, if, 5, (E) T.59.57( ) if, if, 5, 6. Carl notices that for the year 6, he payed $87.8 in Arizona income taes. What was his income for that year? Carl s income for the year 6 was: Less than 85 dollars Between 85 and 95 dollars Between 95 and,5 dollars Between,5 and,5 dollars (E) More than,5 dollars

26 Math Spring 8 Midterm Review Problems Page 6, 5 6. If is a point on the graph of y r? the graph of y r, which one of the following points MUST be on,, 5 5, 5, (E), 5 6. (***) Which one of the following transforms the graph of compression and a horizontal stretch? y f with a vertical y f y f (E) y f y f y f 6. Suppose g ( 7, 7] (, ] ( 6, ] (, ] (E) ( 6, 8] y has a domain of, ] y g? (. What is the domain of 65. (***) The graph of y can be obtained from the graph of y by Shifting up units and reflecting over the -ais. Shifting right units and reflecting over the -ais. Shifting left units and reflecting over the -ais. Shifting right units and reflecting over the y-ais. (E) Shifting left units and reflecting over the y-ais.

27 Math Spring 8 Midterm Review Problems Page 7 y h 66. (***) Consider the table of values for the function given below. h y h? Which one of the following tables of values represents h 8 h h h 6 (E) h.5 5

28 Math Spring 8 Midterm Review Problems Page 8 y 67. Consider the graph of f given below, Which one of the following represents the graph of -6 y f?

29 Math Spring 8 Midterm Review Problems Page (***) Suppose the graph of y following describes the transformations performed? y 7 is transformed into 5 Shift right 5 units, horizontal compression, reflect over the -ais Shift left 5 units, vertical compression by a factor of Shift left 5 units, vertical compression by a factor or Shift right 5 units, vertical compression by a factor of (E) Shift left 5 units, horizontal epansion, reflect over the y-ais, reflect over the -ais, reflect over the y-ais. Which one of the, reflect over the -ais 69. Suppose the graph of following describes the transformations performed? y is transformed into y. Which one of the Shift left units, horizontal epansion, vertical shift up by Shift right units, horizontal epansion, vertical shift up by Shift right units, vertical compression by a factor of, vertical shift up by Shift left units, vertical epansion by a factor of, vertical shift up by (E) Shift right units, vertical epansion by a factor of, vertical shift up by

30 Math Spring 8 Midterm Review Problems Page Spring 8 Midterm Study Guide Answers Question Answer Question Answer D 6 C E 7 D A 8 A B 9 C 5 A B 6 D B 7 E C 8 C A 9 D B D 5 C B 6 B E 7 E C 8 B B 9 A 5 C 5 C 6 A 5 D 7 C 5 B 8 B 5 A 9 A 5 C D 55 D E 56 B C 57 C D 58 D B 59 E 5 A 6 D 6 E 6 D 7 A 6 D 8 C 6 E 9 C 6 B B 65 C D 66 E B 67 A A 68 B E 69 E 5 E