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

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1 MATH 7 - COLLEGE ALGEBRA FINAL REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select from the list of numbers all that belong to the specified set. ) Natural numbers 9,, -, 0, 0 9, 9 ) A) 9, 0 B) 9, 0, 0 9 C) 9, 9 D) 9, 0, 9 ) Rational numbers 9,, -0, 0, 0 -,, 0, 0.09 ) A), B) 9, -0, 0, 0,, 0.09 C) 9, 0, D), 0, 0.09 Write the number in scientific notation. ) A). B). - C). - D). - ) Write the number in standard form. ).00 A).7 B) 0,00 C),0,000 D) 0,0,000 ) Find the percent change if a quantit changes from P to P. Round our answer to the nearest tenth if appropriate. ) P = $, P = $ ) A) -7. B) 9. C) -9. D) 7. Use the information given in the table to solve the problem. ) The table gives the Consumer Price Inde for selected ears. Year CPI What is the percent change (to the nearest tenth of a percent) in prices from 9 to 980? A) 7. % B) 8.8 % C) 9. % D). % ) Solve the problem. 7) An oil spill of 8 cubic centimeters is spilled onto a pond and spreads out in a circular shape having a diameter of 98 centimeters. Approimate the thickness of the oil film to four decimal places, using volume = area thickness(height). A) 8.9 cm B) 0.0 cm C).8 cm D).7 cm 7)

2 Use the information given in the table to solve the problem. 8) The table gives the value of a 97 Chev BelAire in # condition for selected ears. Year Value in dollars ,9,79 Use the concept of an average or mean to estimate the value of a 97 Chev BelAire in # condition in 98. A) $ 9.87 B) $ C) $ 90. D) $ ) Find the mean of the set of data. Round to the nearest tenth. 9), 7,,, 8,,, 9, A). B). C) 9.0 D) 0.9 9) Find the median of the set of data. ), 9, 8,, 87, A) 9. B) 07. C) D) 8 ) Find the distance in the -plane between the two points. Round an approimate result to the nearest hundredth. ) (-, -) and (-, -7) ) A) B) - C). D) Find the midpoint of the line segment joining the two points. ) (-, -9) and (, -7) A) -, - B) - 7, - C) -, - 8 D) -7, - ) Make a scatterplot of the relation. ) {(, ),(-, -),(-, -8),(-8, -),(, ),(, -),(, -),(9, ),(-, -),(-, -)} ) - -

3 A) B) C) D) Evaluate the function as indicated. ) Find f() when f() = + +. A) - B) 0 C) D) ) ) Find f( 7) when f() = +. A) 0 B) C) 9 D) ) Specif the domain of the function. ) f() = 8 - A) > 8 B) 8 C) 8 D) All real numbers ) 7) f() = - 7 A) 7 B) -7 C) All real numbers D) > 0 7)

4 Determine if the relation is a function. 8) 8) A) Not a function B) Function 9) 9) A) Function B) Not a function Find the slope of the line that goes through the pair of points. 0) (, -) and (8, 7) A) Undefined B) C) D) 0) State the slope of the graph of f. ) f() = ) A) 8 9 B) - C) Undefined D) 9 8 Determine if the data in the table is linear or nonlinear. ) A) Linear B) Nonlinear )

5 State whether the given function is linear and constant, linear but not constant, or nonlinear. ) f() = A) Nonlinear B) Linear, but not constant C) Linear, constant D) None of the above ) Solve the problem. ) Compute the average rate of change of f() = + from = to = 8. Round our answer to two decimal places. A).00 B).9 C) 7. D).9 ) The table gives the outside temperature in degrees Fahrenheit on a winter da in Death Valle, California. ) ) Time (A.M.) 7:00 8:00 9:00 :00 :00 Temp Calculate the average rate of change in temperature between 8:00 am and :00 am. Round our answer to two decimal places. A). B). C). D). Identif the slope, -intercept, and -intercept. ) ) A) Slope: ; -intercept: -; -intercept: - B) Slope: -; -intercept: -; -intercept: - C) Slope: -; -intercept: ; -intercept: D) Slope: ; -intercept: ; -intercept:

6 Write the equation of the line whose graph is shown. 7) 7) A) = - - B) = - C) = + D) = - Write a formula for a linear function f whose graph satisfies the conditions. 8) Slope: 7 ; -intercept: - 8) A) f() = B) f() = 7 + C) f() = D) f() = 7 - Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 9) 8 9) A) increasing: [0, ); decreasing: (-, 0] B) increasing: (-, ] [, ); decreasing: [, ] C) increasing: [0, ]; decreasing: (-, 0] [, ) D) increasing: [, ); decreasing: (-, ] Identif where f is increasing or where f is decreasing, as indicated. Round our answer to two decimal places when appropriate. 0) f() = - + ; increasing 0) A) [-, ) B) (-, -] C) (-, ] D) [, )

7 Solve the problem using our calculator. ) The paired data below consist of the test scores of randoml selected students and the number of hours the studied for the test. Use linear regression to find a linear function that predicts a studentʹs score as a function of the number of hours he or she studied. Hours 9 Score ) A) =.7 -. B) = C) =.7 +. D) = Write an equation of the line through the given point with the given slope. Write the equation in slope -intercept form. ) (, ); m = - ) A) = - + B) = - + C) = - + D) = - - Write the slope-intercept form of the equation for the line passing through the given pair of points. ) (8, ) and (, -) A) = B) = C) = D) = 7 - ) Determine the equation of the line described. Put answer in the slope -intercept form, if possible. ) Through (-, ), perpendicular to = 7 A) = 9 + B) = - 9 C) = D) = ) ) Through (, -), parallel to = A) = 8 + B) = C) = - D) = ) Find an equation of the line satisfing the following conditions. If possible, write the equation in slope-intercept form. ) Vertical, passing through (8, -) A) = 8 B) = - C) = 8 D) = - ) Solve the equation smbolicall. 7) = - 7) A) - 9 B) - C) - 7 D) - Solve the problem. Round our answer to the nearest whole number. 8) A tree casts a shadow m long. At the same time, the shadow cast b a 8-cm tall statue is 7 cm long. Find the height of the tree. A) m B) m C) m D) m 8) Solve the problem. 9) In a chemistr class, liters of a % silver iodide solution must be mied with a % solution to get a % solution. How man liters of the % solution are needed? A) liters B) liters C) liters D) liters 9) 7

8 0) A rectangular Persian carpet has a perimeter of inches. The length of the carpet is in. more than the width. What are the dimensions of the carpet? A) Width: 9 in.; length: in. B) Width: 7 in.; length: 0 in. C) Width: 8 in.; length: 7 in. D) Width: 9 in.; length: in. 0) Write the following in interval notation. ) { > } A) (, - ) B) (, ) C) (, ) D) (-, ) ) Epress the following in interval notation. ) A) [-, ) B) [-, ) C) (-, ] D) (-, ] ) Solve the inequalit smbolicall. Epress the solution set in interval notation. ) + > ( + 9) A) (-, ) B) (-, ) C) (, ) D) (, ) ) ) < 8-9 ) A) (, 7 ] B) [, 7 ) C) (7, ] D) [7, ) Evaluate the function f at the indicated value. ) +, if 0 f(7) for f() = -, if 0 < <, if A) B) C) -8 D) 7 ) Sketch a graph of the function. ), if f() = - -, if < )

9 A) B) C) D) Solve the equation graphicall, numericall, or smbolicall. If appropriate, round the solution to hundredths. 7) m + + = 7) A), - B) -.,.7 C)., -.7 D) No solution Solve the inequalit graphicall, numericall, or smbolicall, and epress the solution in interval notation. Where appropriate, round to the nearest tenth. 8) r -. < 8) A) (-, -.) (8., ) B) (-, -8.) (., ) C) (-., 8.) D) (-8.,.) 9) > 8 A) (-, -0.) (-.7, ) B) (-, -.7) (-0., ) C) (-0., -.7) D) (-.7, -0.) 9) 9

10 Use the graph of the quadratic function to determine the sign of the leading coefficient, the verte, and the equation of the ais of smmetr. 0) 0) A) Positive; (-, ); = - B) Positive; (, ); = C) Negative; (-, ); = D) Negative; (-, ); = - Determine the verte of the graph of f. ) f() = ( + ) - A) (-, -) B) (-, -) C) (, ) D) (, -) ) ) f() = ( + ) + ) A) (, -) B) (-, ) C) (-, ) D) (, ) Use the given graph of the quadratic function f to write its formula as f() = a( - h) + k. ) ) A) f() = ( + ) - B) f() = -( - ) - C) f() = ( - ) + D) f() = ( - ) - Solve the quadratic equation. ) = 0 A) -8, B) 8, - C) -, D), - )

11 ) = 9 A) ± B) C) ± D) No real solutions ) ) = 0 ) A) - ± 9 B) - ± C) -8 ± D) - ± Solve the problem. 7) Your compan uses the quadratic model = -. + to represent the average number of new customers who will be signed on () weeks after the release of our new service. How man new customers can ou epect to gain in week? A) 7 customers B) 7 customers C) customers D) customers 7) Use the given graph of f() = a + b + c to solve the specified inequalit. 8) f() < 0 8) - - A) - < < B) < - C) < - or > D) No solutions Solve the inequalit. 9) + - > 0 A) < - or > B) < - C) > D) - < < 9) 0) A) - B) - or C) D) - 0) Use the accompaning graph of = f() to sketch the graph of the indicated equation.

12 ) = f( - ) ) A) B) C) D) Find an equation that shifts the graph of f b the indicated amounts. ) f() = + - 7; right units, down units A) = ( + ) + ( - ) + 9 B) = ( - ) + ( + ) - 0 C) = ( + ) + ( + ) - D) = ( - ) + ( - ) - 0 ) Find the domain of f. ) f() = - - A) { -} B) { } C) { ±} D) { } )

13 Solve the problem. ) A rock is thrown verticall upward from the surface of the moon at a velocit of 8 m/sec. The graph shows the height of the rock, in meters, after seconds. Estimate and interpret the turning point. 00 ) A) The turning point is at approimatel (7., ). This is the point at which the rock reaches its maimum velocit and starts to slow down. B) The turning point is at approimatel (, 0). This is the point at which the rock reaches the surface of the moon again. C) The turning point is at approimatel (7., ). This is the point at which the rock reaches its maimum height and starts to fall back towards the surface of the moon. D) The turning point is at approimatel (, ). This is the point at which the rock reaches its maimum height and starts to fall back towards the surface of the moon. Identif an vertical asmptotes in the graph. ) 8 ) A) = - B) = C) =, = - D) = Use the given functions to find the requested function. ) f() = + 8, g() = Find (fg)(). A) + B) + C) + D) )

14 Identif an horizontal asmptotes in the graph. 7) 98 7) A) = B) = C) = D) None Evaluate as instructed. 8) Evaluate (f+g)(). 8) A) B) - C) 0 D) Solve the problem. 9) Find (f g)() when f() = + and g() = /. A) B) C) 8 D) 9 9) Complete numerical representations for the functions f and g are given. Evaluate the epression, if possible. 70) (f g)() 70) 8 f() g() -7 8 A) Undefined B) 8 C) 0 D)

15 Use the graph to determine whether the function is one-to-one. 7) 7) A) Yes B) No Determine whether or not the function is one -to-one. 7) f() = 7 - A) Yes B) No 7) Find a smbolic representation for f-(). 7) f() = - A) Not a one-to-one function B) f-() = - 7) C) f-() = + D) f-() = + Find either a linear or an eponential function that models the data in the table. 7) ) A) f() = + 7 B) f() = 7() C) f() = (7) D) f() = + 7

16 Graph the eponential function. 7) = 7) A) B) C) D)

17 Determine a formula for the eponential function. 7) (0, ) (, ) 7) A) f() = B) f() = 0. C) f() = D) f() = Use the compound interest formula to determine the final value of the given amount. 77) $,000 at % compounded quarterl for ears A) $,9. B) $,0. C) $,0. D) $,.97 77) 78) $00 at % compounded continuousl for 9 ears A) $8.7 B) $0.0 C) $,7,.7 D) $, ) Evaluate the epression b hand, if possible. 79) log,000 + log 0.00 A) B) - C) -7 D) 7 79) Evaluate the logarithm. 80) log 8 A) - B) 8 C) D) -8 80) Epand the epression. 8) log A) log - log - log B) log + log - log C) ( log )( log ) - log D) log + log + log 8) Write the epression as one logarithm. 8) log b + log b A) log b B) log b C) log b ( + ) D) log b ( + ) 8) Use the change of base formula to approimate the logarithm to four decimal places. 8) log A).78 B) 0.79 C).79 D).7 8) 7

18 Solve the problem. 8) Wind speed varies in the first twent meters above the ground. For a particular da, let f() = 9. ln +. compute the wind speed meters above the ground. At what height is the wind speed meters per second? Round results to the nearest hundredth. A).7 B) 0.7 C) 0. D) 0. 8) Solve the eponential equation. 8) (.) = A). B).77 C).8 D). 8) Solve the logarithmic equation. 8) log ( + 9) = - log A) - B) C) -, D) -, 8) Solve the problem. 87) Suppose A 0 dollars is deposited in a savings account paing.0% interest compounded continuousl. After ears the account will contain A() = A e0.0 dollars. If $80 is initiall 0 deposited in this account, how much would be in the account after ears? Round to the nearest cent. A) $8. B) $. C) $. D) $9. 88) One method to determine the time since an animal died is to estimate the percentage of carbon- remaining in its bones. The percent P in decimal form of carbon- remaining ears is given b P() = e Approimate (to the nearest whole ear) the age of a fossil if there is % of carbon- remaining. A) 78 B),7 C),78 D) -,0 87) 88) A sstem of two linear equations has been solved graphicall. Use the graph to find an solutions. 89) 89) A) (, ) B) No solutions C) (, ) D) Infinite number of solutions Solve the sstem of linear equations. 90) - = 7 - = A) (-9, 0) B) (9, ) C) (, 0) D) No solution 90) 8

19 Solve the problem. 9) There were,000 people at a ball game in Los Angeles. The daʹs receipts were $,000. How man people paid $ for reserved seats and how man paid $ for general admission? A),00 paid $ and,00 paid $ B),000 paid $ and 9,000 paid $ C) 9,000 paid $ and,000 paid $ D),00 paid $ and,00 paid $ 9) Graph the solution set to the inequalit. 9) + - 9) A) B) C) D) 9

20 Match the sstem of inequalities with the appropriate graph. 9) A) B) 9) C) D) Use a graphing calculator to solve the sstem of equations. Round our solutions to one decimal place. 9) z = z = z = 9. A) (.0,., 0.) B) (0., 0., 0.) C) (.8,.8,.) D) (.9,., 0.) 9) Perform the matri operation. 9) Let A = and B = A) 0 - B). Find A + B. 7 C) D) 8 9) Perform the indicated calculation. 9) Calculate a + aa for the matri A = A) - B) - C) 8 D) - 9) 0

21 If possible, find the matri product of AB. 0 97) A = - 0 ; B = ) A) Undefined B) AB = C) AB = - - D) AB = 0 00 Find A-. 98) A = - A) A- = 7-7 B) A- = C) A- = ) Use technolog to calculate det A. 0 99) A = A) B) -7 C) D) 99) Solve the linear sstem for b computing with a calculator. Round to the nearest tenth, as necessar. 0) z = z = z =.0 A) =. B) =. C) =. D) = 0. 0) Answer the question. ) In how man was can ou answer the questions on an eam that consists of multiple choice questions, each of which has answer choices? A) B) 77,987 C) 7,97 D) 77,7 ) ) How man automobile license plates can be made involving letters followed b digits, if letters cannot be repeated ( used more than once ) but digits can be repeated? A),89,00 B),7,00 C) 7,7,000 D),00,000 ) Solve. ) How man was can a president, vice-president, and secretar be chosen from a club with members? A) B) C) 990 D) ) Solve the problem. ) There are people in a club. A committee of persons is to be chosen to represent the club at a conference. In how man was can the committee be chosen? A) B) 7 C) 7,0 D) 90 )

22 ) How man committees of people can be selected from 9 men and 7 women if the committee must have men and women? A) 90 B) 7 C),8 D) 7 ) Find the probabilit of the event. ) A bag contains red marbles, blue marbles, and green marble. What is the probabilit of choosing a marble that is not blue when one marble is drawn from the bag? ) A) B) C) D) Solve the problem. 7) The distribution of B.A. degrees conferred b a local college is listed below, b major. Major Frequenc English,07 Mathematics, Chemistr 8 Phsics 8 Liberal Arts,8 Business,7 Engineering 88 9, What is the probabilit that a randoml selected degree is not in Mathematics? A) 0.0 B) 0. C) 0.78 D) 0.8 7)