FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.


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1 FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) Does the table define as a function of? A) Yes B) No State whether the graph is or is not that of a function. ) A) No B) Yes Find the domain of the function. 3) =  7 A) (7, ) B) all real numbers ecept 7 C)[7, ) D) (, ) Decide whether or not the equation defines as a function of. 4) =  9 A) No B) Yes ) The polnomial gives the predicted sales volume of a compan, in millions of items, where is the number of ears from now. Determine the predicted sales ears from now. Round our answer to the nearest hundredth million. A) $4.89 million B) $11.7 million C) $3.94 million D) $8.86 million 6) The polnomial function I(t) = 0.1t + 1.t represents the earl income (or loss) from a real estate investment, where t is time in ears. After what ear does income begin to decline? A) 6. B) 7. C) D) 1 Find the slope of the line (if it eists) and the intercept (if it eists). 7) = A) Slope 9, intercept (0, 3) B) Slope 9, intercept (0, 3) C) Slope 3, intercept (0, 9) D) Slope 3, intercept (0, 9) 1
2 8) The following graph shows the stock price of a new internet compan over the first 18 months after the initial public offering of its stock. Stock Price (in dollars) Month How man months was the stock price $40 during the initial 18 month period? A) 1 month B) months C)3 months D) 4 months 9) The bar graph below gives the number of births in Count A for the ears 1960 to If the number of births in thousands in Count A is the function B(t), where t is in ears, find B(1960) and eplain its meaning. A) B(1960) = 1.693; In 1960 there were births in Count A. B) B(1960) =.190; In 1960 there were.190 births in Count A. C)B(1960) =.190; In 1960 there were,190 births in Count A. D) B(1960) = 1.693; In 1960 there were 1,693 births in Count A. 10) The cost of a rental car for the weekend is given b the function C() = , where is the number of miles driven. Find the slope of the graph of this function and interpret it as a rate of change. A) 141; The cost of the rental car increases b $141 for each mile driven. B) 0.6; The cost of the rental car decreases b $0.6 for each mile driven. C)141; The cost of the rental car decreases b $0.6 for each mile driven. D) 0.6; The cost of the rental car increases b $0.6 for each mile driven. 11) The cost of a rental car for the weekend is given b the function C() = , where is the number of miles driven. Find and interpret the Cintercept of the graph of this function. A) 14; The cost of the rental car increases b $14 for each mile driven. B) 0.7; The cost of the rental car increases b $0.7 for each mile driven. C)14; There is a flat rate of $14 to rent a car in addition to the charge for each mile driven. D) 0.7; There is a flat rate of $0.7 to rent a car in addition to the charge for each mile driven.
3 Find the slope of the line through the pair of points. 1) (, 4) and (4, 8) A) B) 1 C)  1 D) 1 1 Find the  and intercepts of the graph of the given equation, if the eist. Then graph the equation. 13) 63 = 9 A) (3, 0); 0,  3 B)  3, 0 ;(0, 3) C)  3, 0 ;(0, 3) D) (3, 0); 0, Write the equation of the line with the given conditions. 14) passing through (4, ) and parallel to the line with equation 4 + = 4 A) = 418 B) = C) = D) = Write the equation of the line using the information given about its graph. 1) Slope  7 3, intercept 0, 8 8 A) = B) = C) = D) =
4 16) Suppose the monthl cost for manufacturing bar stools is C() = , where is the number of bar stools produced each month. Find and interpret the marginal cost for the product. A) $48 per bar stool; Manufacturing one additional bar stool decreases the cost b $48. B) $38 per bar stool; Manufacturing one additional bar stool increases the cost b $38. C) $38 per bar stool; Manufacturing one additional bar stool decreases the cost b $38. D) $48 per bar stool; Manufacturing one additional bar stool increases the cost b $48. Write an equation of the line through the given point with the given slope. Write the equation in slopeintercept form. 17) (4, 4); m =  A) = B) = C) = D) = Write the slopeintercept form of the equation for the line passing through the given pair of points. 18) (8,) and (0, ) A) = B) = C) = + D) = ) Using a phone card to make a long distance call costs a flat fee of $0.66 plus $0.14 per minute starting with the first minute. What is an equation of the form = m + b for this situation? A) = B) = 0.14 C) = D) = ) The following data show the list price,, in thousands of dollars, and the dealer invoice price,, also in thousands of dollars, for a variet of sport utilit vehicles. Find a linear equation that approimates the data, using the points (16., 16.1) and (0.0, 18.3). List Price Dealer Invoice Price A) = B) = C) = D) = Solve the equation. 1) = A) 3 14 B) 4 6 C) D) Find the zero of f. ) f() = A)  B) 8 C)8 D) 3) Suppose the sales of a particular brand of appliance satisf the relationship S() = , where S() represents the number of sales in ear, with = 0 corresponding to 198. In what ear would the sales be 70? A) 199 B) 1994 C) 1993 D) 199 4
5 Two linear functions, 1 and are graphed in a viewing window with the point of intersection of the graphs given in the displa at the bottom. Use the intersection method to solve the equation 1 =. 4) A) 3 B) 1 C) 4 D)  Solve the formula for the specified variable. ne ) I = nr + R for n A) n = IR Ir  E B) n = R Ir  E C)n = IR Ir + E D) n = IR(Ir  E) Use the data shown in the scatter plot to determine whether the data should be modeled b a linear function. 6) A) No, data points do not lie close to a line B) Yes, approimatel linear C) Yes, eactl linear Write the bestfit linear model for the data. 7) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Find a linear function that predicts the number of products sold as a function of the cost of advertising. Cost Number A) = B) = C) = D) = Does the sstem have a unique solution, no solution, or man solutions? 8)  = 4 + = 18 A) Man solutions B) No solution C) A unique solution Solve the sstem of equations b substitution, if a solution eists. 9)  4 = = 9 A) = 1, = B) No solution C) =, = 1 D) = , =
6 30) The paired data below consist of the test scores of 6 randoml selected students and the number of hours the studied for the test. The linear model for this data is = , where is number of hours studied and is score on the test. Use this model to predict the score on the test of a student who studies 7 hours. Hours Score A) 77.8 B) 79.8 C) 69.8 D) 74.8 Solve the sstem of equations b elimination, if a solution eists. 31) + 4 = = 30 A) = 1, = B) = 0, = 6 C) = 6, = 0 D) No solution To find the number of units that gives breakeven for the product, solve the equation R = C. Round our answer to the nearest whole unit. 3) A manufacturer has total revenue given b the function R = 90 and has total cost given b C = ,000, where is the number of units produced and sold. A) 140 units B) 407 units C) 1164 units D) 40 units Solve the sstem of equations graphicall, if a solution eists. 33) 3 + = = 38 A) = , = 3 B) = 6, = 6 C) = , = 6 D) =, = 6 34) A certain product has suppl and demand functions given b p = 7q + 1 and p = 394q, respectivel, where p is the price in dollars and q is the quantit supplied or demanded at price p. What price gives market equilibrium? A) $8 B) $196 C) $17 D) $17 3) Suppose that the number of inhabitants of Countr A is given b = million, and the number of inhabitants of Countr B is given b = million, where is the number of ears since Find the ear in which the number of inhabitants of Countr A equals the number of inhabitants of Countr B. A) 198 B) 1987 C) 1983 D) 1981 Solve the inequalit. 36) 13 < A) 6 <  B) 6  C) 6 <  D) 6 < <  37) A salesperson has two job offers. Compan A offers a weekl salar of $300 plus commission of 1% of sales. Compan B offers a weekl salar of $600 plus commission of 6% of sales. What is the amount of sales above which Compan A's offer is the better of the two? A) $000 B) $10,000 C) $00 D) $100 6
7 Solve the inequalit and draw a number line graph of the solution. 38) 9a  > 10a + 4 A) (1, ) B) (, 9) C)(9, ) D) (, 1) Determine if the graph of the function is concave up or concave down. 39) = A) Concave down B) Concave up Determine if the verte of the graph is a maimum point or a minimum point. 40) = A) Maimum B) Minimum 41) At Allied Electronics, production has begun on the X1 Computer Chip. The total revenue function is given b R() = and the total cost function is given b C() = , where represents the number of boes of computer chips produced. The total profit function, P(), is such that P() = R()  C(). Find P(). A) P() = B) P() = C)P() = D) P() = ) A projectile is thrown upward so that its distance above the ground after t sec is given b h(t) = 11t + 64t. After how man seconds does it reach its maimum height? A) 1 sec B) 6 sec C)4 sec D) 18 sec Use factoring to solve the equation. 43) 1d + 4d + 9 = 0 A) 3, 1 B) 3, C)  3,  1 D)  3,  1 Find the intercepts. 44) = A) (6, 0), (, 0) B) (10, 0), (, 0) C)( 1, 0) ( 1, 0) D) (6, 0), (, 0) 7
8 Provide an appropriate response. 4) Write the equation of the quadratic function whose graph is shown. 8 6 (3, ) 4 (, 1) A) = ( + 3) + B) = (  3) + C) = (  3) + D) = (  3) + Use the square root method to solve the equation. 46) + = 1 A) ±7 B). C)±6 D) 7 Use the quadratic formula to solve the equation. 47) = 0 A)  6,  1 B) , C), 4 3 D), ) The function defined b D t = 13t  73t gives the distance in feet that a car going approimatel 0 mph will skid in t seconds. Find the time it would take for the car to skid 76 ft. Round to the nearest tenth. A) 9. sec B) 8. sec C)9.4 sec D) 9.6 sec Find the requested value. 49), if 1 f(1) for f() =  7, if > 1 A) B) 8 C)  D) 6 Determine if the function is increasing or decreasing over the interval indicated. 0) = 7 ; > 0 A) Decreasing B) Increasing 1) A manufacturer's cost is given b C = 00 3 n + 00, where C is the cost and n is the number of parts produced. Find the cost when 1 parts are produced. A) $100 B) $700 C) $790 D) $140 8
9 Graph the function. ) f() = 3, if 11 , if < 1 A) B) C) D) Find a power function that models the data in the table. Round to three decimal places if necessar. 3) A) = B) = C) = D) = Find a quadratic function that best fits the data. Give answers to the nearest hundredth. 4) A) = B) = C) = D) = ) A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. Number of Desks Produced Profit (Thousands) Find a quadratic function to model the data, and use the model to predict the profit if 40 desks are made. A) Almost $44,000 B) Almost $4,000 C) Just over $40,000 D) Just under $4,000 9
10 6) Assume it costs 34 cents to mail a letter weighing one ounce or less, and then 8 cents for each additional ounce or fraction of an ounce. Write a piecewisedefined function P() that represents the cost, in cents, of mailing a letter weighing between 0 and 3 ounces. A) B) C) P() = P() = 34 if 1 < 6 if < 3 90 if 3 < 4 6 if 1 90 if 1 < 118 if < 3 D) P() = P() = 34 if < 1 6 if 1 < 90 if < 3 34 if 1 6 if 1 < 90 if < 3 7) The percent of people who sa the plan to sta in the same job position until the retire has decreased over recent ears, as shown in the table below. Year Percent Find a power function that models the data in the table using an input equal to the number of ears from A) = B) = C) = D) = Fill in each blank with the appropriate response. 8) The graph of = ( ) + 7 can be obtained from the graph of = b shifting horizontall units to the, verticall stretching b a factor of, reflecting across the ais, and shifting verticall units in the direction. A) ; left; ; ; 7; upward B) ; right; 7; ; ; downward C); right; ; ; 7; upward D) ; right; 7; ; ; upward Write the equation of the graph after the indicated transformation(s). 9) The graph of = is shifted 8 units to the left and units downward. A) = ( + 8)  B) = ( + )  8 C) = (  ) + 8 D) = (  8)  Write the equation of the function g() that is transformed from the given function f(), and whose graph is shown. 60) f() = A) = ( + 3) B) = (  3) C) = (  )  3 D) = (  3)
11 Determine whether the graph of the given equation is smmetric with respect to the ais, the ais, and/or the origin. 61) f() = A) ais, origin B) ais C) ais, ais D) Origin Determine whether the function is even, odd, or neither. 6) f() = A) Even B) Odd C) Neither For the pair of functions, perform the indicated operation. 63) f() =  4, g() = Find (f + g)(). A) + 6 B) 6 + C) D) 4 Find the specified domain and epress it in interval notation. 64) For f() =  and g() = + 3, what is the domain of f g ()? A)  3, B) (, ) C) , 33, D) (, ) Find the requested composition of functions. 6) Given f() = 4 + and g() = 6 +, find (g f)(). A) B) C) D) ) AAA Technolog finds that the total revenue function associated with producing a new tpe of computer chip is R() = , and the total cost function is C() = + 1, where represents the number of units of chips produced. Find the total profit function, P(). A) P() = B) P() = C)P() = D) P() = Determine whether (f(g()) = and whether (g (f()) =. 67) f() = 3 + 6, g() = 36 A) Yes, no B) No, es C)Yes, es D) No, no Decide whether or not the functions are inverses of each other ) f() =, g() = + 7 A) Yes B) No 69) The suppl function for a product is p() = , where is the number of thousands of units a manufacturer will suppl if the price is p() dollars. Find the inverse of this function. A) p1() = 3(  40) B) p1() = 340 C)p1() = 3 (  40) D) p1() =
12 Determine if the function is a growth eponential or a deca eponential. 70) = A) Growth B) Deca Write the logarithmic equation in eponential form. 71) log 4 16 = A) 4 = 16 B) 4 = 16 C)416 = D) 16 = 4 Write in logarithmic form. 7)  = 1 4 A) log = B) log  = 1 4 C) log 1/4 =  D) log 1 4 =  Find the value of the logarithm without using a calculator. 73) log 8 3 A) 4 3 B) 3 C) 4 D) 3 Use the properties of logarithms to evaluate the epression. 74) log (7) A) 7 B) C)7 D) 1 Solve. 7) Given that loga = and loga3 = , find loga7. A) B).0333 C) 0.49 D) 1.87 Rewrite the epression as the sum and/or difference of logarithms, without using eponents. Simplif if possible. 76) log 9 16 A) log 9  log 9 16 B) log 9 log 9 16 C) log 9 + log 9 D) log log 9 Rewrite as a single logarithm. 77) 1 log log log A) log 17/6 B) 7 6 log 8 C)log 9/ D) log 7 78) The sales of a new product (in items per month) can be approimated b S() = log(3t + 1), where t represents the number of months after the item first becomes available. Find the number of items sold per month 3 months after the item first becomes available. A) 17 items per month B) 77 items per month C)10,7 items per month D) 7 items per month 1
13 79) An earthquake was recorded as 10.8 times more powerful than a reference level zero earthquake. What was the magnitude of this earthquake on the Richter scale? R = log I I0. A).8 B) 4. C) 13.4 D) 1.8 Solve the equation. 80) 10 = 30 (Round to two decimal places.) A) 3.00 B) 1.48 C) 0.68 D).10 Use a change of base formula to evaluate the given logarithm. Approimate to three decimal places. 81) log 8.8 (.1) A) B).931 C) 0.3 D) 0.39 Solve the equation. If necessar, round to thousandths. 8) (  3) = A) 1.00 B) C).6 D) Solve the equation. 83) 8 ln = 7 A) 6e B) e1 C)e7/8 D) e 7 8 Solve the equation. Give an eact solution. 84) log (  9) = 1  log A) 1, 10 B) 10, 1 C) 10 D) 10 8) Find the amount of mone in an account after 7 ears if $400 is deposited at 6% annual interest compounded quarterl. A) $ B) $ C) $3630. D) $ ) At the end of t ears, the future value of an investment of $3000 in an account that pas 8% APR compounded monthl is S = t dollars. Assuming no withdrawals or additional deposits, how long will it take 1 for the investment to reach $9000? Round to three decimal places. A) ears B) ears C) ears D) ears 87) Find the eponential function that models the data in the table below. f() A) f() = 7 0. B) f() = C)f() = D) f() =
14 88) Find the logarithmic function that models the data in the table below A) f() = ln B) f() = ln C)f() = log D) f() = ln 89) Find an eponential function that models the data below and use it to predict about how man books will have been read in the eighth grade. Grade Number of Books Read A) 1883 books B) 3000 books C) 00 books D) 1000 books 90) Barbara knows that she will need to bu a new car in ears. The car will cost $1,000 b then. How much should she invest now at 10%, compounded quarterl, so that she will have enough to bu a new car? A) $11,69.7 B) $13,60.44 C) $1,311.0 D) $13, ) Joe invested $00 at 9% compounded semiannuall. In how man ears will Joe's investment have quadrupled? Round our answer to the nearest tenth of a ear. A) 1.4 ears B) 8.8 ears C).0 ears D) 1.7 ears Determine whether the polnomial function is cubic or quartic. 9) g() = A) Cubic B) Quartic Find the cubic or quartic function that models the data in the table. 93) (Cubic) A) = B) = C) = D) = ) (Quartic) A) = B) = C) = D) =
15 Answer Ke Testname: FINAL EXAM PREP 1) A ) A 3) A 4) B ) C 6) B 7) C 8) C 9) D 10) D 11) C 1) C 13) A 14) B 1) A 16) B 17) D 18) B 19) C 0) A 1) D ) A 3) D 4) B ) A 6) B 7) C 8) B 9) C 30) D 31) B 3) B 33) C 34) D 3) D 36) C 37) A 38) C 39) B 40) B 41) D 4) A 43) C 44) A 4) B 46) A 47) B 48) B 49) C 0) B 1
16 Answer Ke Testname: FINAL EXAM PREP 1) B ) D 3) A 4) D ) B 6) D 7) B 8) C 9) A 60) D 61) D 6) B 63) C 64) C 6) A 66) C 67) C 68) B 69) A 70) B 71) B 7) D 73) B 74) C 7) D 76) A 77) A 78) B 79) A 80) B 81) A 8) B 83) C 84) D 8) D 86) D 87) B 88) A 89) A 90) C 91) D 9) A 93) B 94) C 16
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