Unit 3 Exam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Unit Eam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Some Useful Formulas: Compound interest formula: A=P + r nt n Continuously compounded interest formula: A=Pe rt Find all numbers that must be ecluded from the domain of the rational epression. - 8 ) , 5-8, -5 ) ) , -5 0, 5 ) ) , -, 6 ) ) + 7-6, ) Multiply or divide as indicated. Simplify completely. 5) ( - ) ( - ) ) 6) ) 7) ) ( + ) + (- - )

2 8) ) ( + 9) ) ) Add or subtract as indicated. 0) ) - ( + )( - ) - + ( + )( - ) ( + )( - ) - - ( + )( - ) ) ) ( + )( - 6)( - ) ( - )( + 6)( + ) ) ) 8 - ( - )( + )( - ) 9 - ( - )( + )( - ) - 9 ( - )( + )( - ) 9 - ( - )( - ) ) ) ) ) ) ) - 8 ( - 6) - 8 (6 - ) 8 - (6 - ) 8 - ( - 6)

3 Solve the equation. 6) + = ) - 5 {-} {} 7) m + m - m - + m - 8 m = + 8m + 6 m + m - 8 { -0 } { -0 } { 0 } { - } 7) 8) 9) y y - = 0 y - 6 {8} { } {5} {-8} = {0} {-6} {} 8) 9) Find the vertical asymptotes, if any, of the graph of the rational function. 0) h() = ( - ) = 0 and = - = = 0 and = no vertical asymptote ) f() = + = = -, = = - no vertical asymptote ) g() = - = =, = - =, = -, = 0 no vertical asymptote 0) ) ) ) = - = -, = -9 =, = 9, = - =, = 9 ) ) g() = - = 0 and = - = 0 and = = no vertical asymptote )

4 Find the horizontal asymptote, if any, of the graph of the rational function. 5) g() = ) y = 5 6 y = y = 0 no horizontal asymptote 6) f() = + 5 6) y = - 5 y = 0 y = no horizontal asymptote 7) g() = + 7) y = y = y = 0 no horizontal asymptote -5 8) f() = ) y = - y = - y = 0 no horizontal asymptote Use the horizontal line test to determine whether the function is one-to-one. 9) 9) Yes No

5 0) 0) No Yes ) ) No Yes ) ) No Yes Find the inverse of the one-to-one function. ) f() = ( + 8) ) f - () = + 8 f - () = - 5 f - () = - 8 f - () = - 8 5

6 ) f() = 7 - ) f - () = 7y + 7 f - () = f - () = f - () = 7-5) f() = ( + 5) 5) f - () = + 5 f - () = - 5 f - () = - 5 f - () = - 5 6) f() = ) f - () = f - () = f - () = f - () = 8-5 Write the equation of the graph in its final position. 7) The graph of y = e is translated 6 units to the right and then units upward. 7) y = e y = e y = e y = e The graph of an eponential function is given. Select the function for the graph from the functions listed. 8) 8) f() = f() = - f() = - f() = + 6

7 9) 9) f() = - f() = - - f() = - f() = 0) 0) f() = - - f() = - f() = f() = - Solve the problem.. ) An initial investment of $80 earns interest for 7 years in an account that earns % interest, compounded quarterly. Find the amount of money in the account at the end of the 7 year period. $8. $9.5 $75. $695.0 ) Suppose that you have $000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded continuously or 7.6% compounded semiannually? Both investment plans yield the same return. $000 invested at 7.6% compounded semiannually over 9 years yields the greater return. $000 invested at 7.5% compounded continuously over 9 years yields the greater return. ) Find the accumulated value of an investment of $0,000 at % compounded semiannually for 8 years. $50,807.0 $9,00.00 $, $9,59.6 ) Suppose that you have $0,000 to invest. Which investment yields the greater return over 7 years: 6.6% compounded monthly or 6.7% compounded quarterly? Both investment plans yield the same return. $0,000 invested at 6.6% compounded monthly over 7 years yields the greater return. $0,000 invested at 6.7% compounded quarterly over 7 years yields the greater return. ) ) ) ) 7

8 Solve the equation. 5) log / = - 5) ) log ( + ) - log ( - ) = log 6) {0} {-0} 7) log = log 5 + log ( - ) 7) {-0} {0} - 5 8) log 5 ( + 5) = log 5 ( + ) 8) 7 {} {0} Simplify the epression. 9) 8 log 8 (6) 9) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 50) log 6 50) ) log 7 5) ) log (.85) 5) Solve the equation. 5) 9 - =() 5) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 5) + = ) {ln 5 - ln } {7 ln 5-5 ln } ln 5 ln 5 - ln ln - ln

9 55) 5 9 =.7 55) ln.7.7 ln 9 9 ln.7 ln.7 9 ln 5 ln 5 ln 5 5 ln 9 Solve the equation by epressing each side as a power of the same base and then equating eponents. 56) ( + 6) = 7 56) 9 {} {-} {9} 57) 6 = 6 57) {} 5 58) e + = e 58) {-} {5} {-5} {} Solve the equation. Round your answer to three decimal places. 59) (-) = 9 59) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 60) e = 7 60) Rewrite the epression as a single logarithm. 6) 6 log m (y )- log m ( ) 6) logm y6 5 logm 6y logm y6 logm y6 6 6) ln + 9ln y 6) ln y 9 ln ( + 9y) ln 9y ln y 9 6) log b y + 6log b z 6) log b y z 6 0log b yz log b yz log b (yz) 0 6) (log 7 (r - ) - log7 r) 6) log7 r - r log7 r - r log7 r - r log7 r - r 9

10 Rewrite the epression as a sum or difference of logarithms or multiples of logarithms. 65) log 9 y log () + 8 log (y) - log (7) 9 log () - 8 log (y) - log (7) (9 log ())(8 log (y)) - log (7) 9 log () + 8 log (y) + log (7) 65) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 66) log y 8 66) log - 8 log y 8 log y - log log + 8 log y 8 log ( y ) 67) log 67) log - - log log - - log 8 68) log y 68) 8 log - log y - log 8 log - log y - log 8 log - log y - log 8 log - log y - log Use properties of logarithms to epand the logarithmic epression as much as possible. 69) log ) log log 6 log log 6 log 6 0 log log 6 70) log ) log 5 ( + 5) - log 5 log 5 ( + 5) + log 5 log 5 ( + 5) - log 5 log 5 - log 5 ( + 5) 7) log w 7 log w 7 + log w + log w log w 7 - log w log w 7 + log w - log w log w 7) 0

11 Determine whether the given ordered pair is a solution of the system. 7) (-, -) - y = -6 + y = - solution not a solution 7) (, ) - y = - y = 7 not a solution solution 7) (-5, ) = - - y = -8 - y not a solution solution 7) 7) 7) Solve the following systems of linear equations. 75) - y = - + y = 5 75) No Solution (, 5) (9, 8) (8, 9) 76) - + y = - y = 0 {(-6, -8)} {(-8, 6)} {(-8, -6)} {(-7, -6)} 76) 77) y = 5-5y + 5 = -95 {(, -)} {(-, -)} {(-, -)} 77) 78) 8 + 8y = 8 5 -y = 8 Infinitely Many Solutions {(, )} No Solution {(, )} 78) 79) 6 + y = 9-7y = -7 {(0, 0)} {(0, )} {(, 0)} {(, )} 80) + y = 0 + y = {(-, 6)} {(-6, )} {(6, -)} {(-6, )} 8) - + 5y = y = {(-, -)} {(, )} {(, -)} {(-, )} 79) 80) 8)

12 Solve the problem. 8) The sum of two numbers is. If one number is subtracted from the other, their difference is 5. Find the numbers. -8, -7 8, -7 0, 8, 7 8) One number is 9 less than a second number. Twice the second number is more than times the first. Find the two numbers. -5 and -6 - and - 5 and - and -5 8) There were 60 people at a play. The admission price was $ for adults and $ for children. The admission receipts were $950. How many adults and how many children attended? 0 adults, 0 children 7 adults, 9 children 55 adults, 75 children 0 adults, 0 children 85) A vendor sells hot dogs and bags of potato chips. A customer buys hot dogs and bags of potato chips for $0.75. Another customer buys hot dogs and 5 bags of potato chips for $9.75. Find the cost of each item. $.00 for a hot dog; $.50 for a bag of potato chips $.75 for a hot dog; $.50 for a bag of potato chips $.5 for a hot dog; $.75 for a bag of potato chips $.75 for a hot dog; $.5 for a bag of potato chips 86) A rectangular lot whose perimeter is 500 feet is fenced along three sides. An epensive fencing along the lot's length costs $ per foot, and an inepensive fencing along the two side widths costs only $6 per foot. The total cost of the fencing along the three sides comes to $50. What are the lot's dimensions? Length 8 ft; Width 0 ft Length 00 ft; Width 00 ft Length 50 ft; Width 00 ft Length 5 ft; Width 96 ft 8) 8) 8) 85) 86)

13 Answer Key Testname: CA UNIT PRACTICE EXAM FALL0V59NOREGEN ) D ) A ) C ) B 5) B 6) C 7) A 8) B 9) A 0) D ) D ) B ) D ) D 5) A 6) D 7) B 8) D 9) D 0) B ) D ) B ) D ) C 5) A 6) C 7) A 8) C 9) B 0) B ) B ) A ) D ) B 5) B 6) D 7) D 8) B 9) B 0) B ) C ) C ) A ) C 5) D 6) B 7) C 8) D 9) D 50) C 5) D 5) B 5) D 5) B 55) A 56) C 57) D 58) C 59) D 60) D 6) D 6) D 6) A 6) B 65) A 66) A 67) C 68) A 69) D 70) C 7) C 7) B 7) A 7) B 75) D 76) C 77) C 78) A 79) B 80) C 8) C 8) B 8) D 8) D 85) D 86) C

MATH 035 and MATH 043 REVIEW for FINAL EXAM

MATH 035 and MATH 043 REVIEW for FINAL EXAM MATH 03 and MATH 043 REVIEW for FINAL EXAM MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Solve and graph: -20 8x - 4 and 2x + 7 < 11 1) (-2,