COLLEGE ALGEBRA FINAL REVIEW 9) 4 = 7. 13) 3log(4x 4) + 8 = ) Write as the sum of difference of logarithms; express powers as factors.

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1 Solve. 1) x 1 8 ) ( x ) x x 9 ) x 1 x 4) x + x 0 ) x + 9y 6) t t 4 7) y 8 4 x COLLEGE ALGEBRA FINAL REVIEW x 8) 81 x + 9) x 10) e 10 11) solve for L P R K M + K L T 1) a) log x log( x+ 6) 1 b) log x+ log( x+ 4) log1+ log 1) log(4x 4) Write as a single logarithm and simplify, if possible. 14) log log ) ln x + ln y ( lnx + lny) 16) Write as the sum of difference of logarithms; express powers as factors. Simplify the following: 17) ( x + ) ( x x + 1) ) ln x e ln xy z 18) ( y 4) 19) ( u + )( u ) ( u + 4) x y z 0) x y z ab 8xy 1) xy ab ) ( 1 1) 1 y x 4) 71 log t t 4x ) ln e 6) ( + i ) ( i)( + i) 7) + i i

2 Evaluate to decimal places. 8) log 7 9) e log e 0) 4 + ln 7 Given: log a. and log a Find the following to decimal places. 1) log a ) log a 7 ) loga 1 loga 4) log a 7 ) Convert to exponential equation ln x 6) Find the equation of the line (in slope-intercept form) that passes through (,-1) and (,-). 7) Find the distance between the points (7,-) and (8,-) Let f ( x) x x + 4. Find the following: 8) f ( ) 9) f ( t 1 ) 40) f ( x + h ) f ( x ) h Solve the following inequalities. Write the solutions in interval notation: 41) x 6x + 7 x 4) 1 4) x + 1 > xx ( + ) x + 1 x 46) > 1 4) 7 9 x 44) k > k + 47) For the function f( x) x 4x+ a) Find the vertex b) Find the line of symmetry c) Give the x, y coordinates of the maximum or minimum point d) Give the range of the function

3 Given the following cost and revenue functions, find the profit function and find the maximum profit as well as the number of units needed to obtain the maximum profit. 48) R ( x) x x ; C( x) x 8x 7 49) Sales of Packard Bell computers have grown exponentially. The total revenue function, in millions, is given by Rt ( ) 0.18(1.4) t where t is the number of years since Find Packard Bell s revenues in 1999, 00, and 00 assuming the growth rate remains the same. When will its sales revenue to $10 million? 0) A company finds that its costs follow the function Cx ( ).00x 1x+ 4,000 where x is the number of items made. How many items should it make to minimize its costs? 1) The sum of the width and length of a parallelogram is 90 cm. Find the dimensions for which the area is a maximum. Find all asymptotes of the functions. ) ) x + 4x + g ( x) x + 9 f ( x) x x x 11 4) Use your calculator to graph f( x) 1/( x 4) a) What is the y-intercept, if any? b) What is the x-intercept, if any? c) What is (are) the vertical asymptote(s), if any? d) What is the horizontal asymptote, if any? ) Find the center and the radius of the circle x + y 8x+ y ) What is the domain of f( x) x 7 7) What is the domain of f( x) x + x 16

4 8) Find the equation of the line (in slope-intercept form) that passes through (,-4) and is parallel to x y ) Find the equation of the line passing through the point (-1,) and perpendicular to the line x y 9 x Given f ( x) and g( x) x 1. Find the following: 60) f ( x) + g( x) 6) ( f g)( x) 61) ( f g)( x) 1 6) f ( x ) 64) Given f( x) x and gx ( ) x 1. Find the following: a) ( f g)() b) ( fg)( 1) 1 c) ( f / g )( ) d) ( f g)( ) 6) Find the inverse of 6 f( x) x + 66) Find the inverse of f( x) x+ 4 Given f ( x) x x 1x + x ) Is - a zero of f ( x)? 68) Find all the zeros of f ( x) 69) Use synthetic division to determine whether is a zero of f( x) x + x x ) Find all the zeros of 4 f( x) x x x + 1x ) Find all zeros of f( x) x x + 4x 0. Graph the following. State the domain, range, relative extrema, and intervals of increasing/decreasing. 7) f ( x) 8x x 7x +

5 7) Write the equation of the function which has the same shape as f( x) x but has been shifted 7 units to the right and up units and then reflected about the x axis. 74) Use your calculator to graph f( x ) 4 x. What is the domain? What is the range? 7) Suppose $,000 is invested at k percent, compounded continuously, and grows to $,98.6 in 7 years. a) What is k? b) How much will be in the account after 9 years? c) How long does it take the money to double? 76) A piece of charcoal is found to contain 0% of its carbon-14. If the decay rate of carbon-14 is , how old is the piece of charcoal? 77) The volume V of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If V1 cubic centimeters when T 4º and P0 kg/square centimeters, what is the volume when T0º and P1 kg/square centimeters? Use the given table to answer questions for a given rational function f( x) where f( x ) Y 1. 78) a) List the x-intercepts, if any, of f( x ). Write as an ordered pair. b) List any y-intercepts, if any, of f( x ). Write as an ordered pair. 79) Find the following: a) f ( 1) b) x such that f( x ) 4 80) Are there any restrictions for f( x )? If so, what are they? Explain.

6 x, x 4. x ± 9 y 6. ± 7i 4 7. y 10 /, y COLLEGE ALGEBRA REVIEW ANSWERS x 8y. x z x yb 1 7a xy y x x 8. x 9. x log81 + log x a) log 7 log RKT L MKT + PT + K x b) x 1 1. x log ln x y ln x+ ln y ln z 4x 7x y 4 y i e x 6. y x t 7t x + h 41. (, ] 4. (, ) (1, ) 4. [ 8,0] 19. u 4 16

7 44., and ( 1, ) 4. (,0) ( 0,1 ] 46., a) (,6) b) x c) max(,6) d) y units; $1 max. profit $1.16 Million; 00 $4.817 Million; 00 $ Million; 10 Million sometime in items 1. 4 cm. by 4 cm.. V.A.: x 9 ; H.A.: none S.A.: y x 1. V.A.: x, x ; H.A.: y 1 x 4. a) b)none c) x 4 d) as 4 y 0. C(4, 1), r 6. 7 x 7. x ± 4 8. y x 7 9. y x x x 9 x x 7 1 x + 6. f ( x) 64. a) b) c) undefined d) f 67. Yes 1 6 ( x) [8, 0] x 1 f ( x) x 68.,,, 69. not a zero 70. 1,, 71., i, i 7. D: (, ) ; R: (, ) ; rel. max. of x 0. 70; rel. min. of x ; inc.: (, 0. 70) ( , ) ( 0. 70, ) 7. x 7, ; dec.: 74. Domain: (, ) ; range: (0, ) 7. a) k.0714 b)$44.80 c) 1.1 yr ,0 years old cm 78. a) There are no x-intercepts in the table (where y 0). If this was a polynomial function, then the Intermediate Value Theorem says there s a zero between 1 and (but this is a rational function); b) (0,1.)

8 79. a) 1.6; b) 80. At x 4, there is an error for y. This means that 4 is not in the domain of f( x )