6. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given by

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1 MATH 34 - College Algebra Review for Test 3 Section 4.6. Let f ( ) = (a) What is the domain? (b) Give the -intercept(s), if an. (c) Give the -intercept(s), if an. (d) Give the equation(s) of the vertical asmptote(s), if an. (e) Give the equation(s) of the horizontal asmptote(s), if an.. Let f ( ) = (a) What is the domain? (b) Give the -intercept(s), if an. (c) Give the -intercept(s), if an. (d) Give the equation(s) of the vertical asmptote(s), if an. (e) Give the equation(s) of the horizontal asmptote(s), if an Let f ( ) = 5. (a) What is the domain? (b) Give the -intercept(s), if an. (c) Give the -intercept(s), if an. (d) Give the equation(s) of the vertical asmptote(s), if an. (e) Give the equation(s) of the horizontal asmptote(s), if an. 4. Use transformations of the memorized graph for = to graph = + on the coordinate sstem at the right. 5. Use transformations of the memorized graph for = to graph = 4 on the coordinate sstem at the ( + ) right.

2 MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. of 6 6. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given b the formula D( ) = 500, where is the grade (slope) of the road. If the braking distance is feet, what is the grade of the road? Round our answer to the nearest tenth of a percent. Section 4.7 (Ecluding Polnomial Inequalities) 7. Solve for : = 5 8. The graph of f () is shown at the right. For what values of is f () 0? Give our answer in interval notation. (Note: All intercepts and asmptotes occur at integers.) 9. Solve for and give our answer in interval notation: 3 < 0 0. Solve for and give our answer in interval notation: Section 4.8. Use laws of eponents to write the following as a single power of : Solve for : = 3. Solve for : 5 + = 3 4. Suppose that the surface area S of a bird's wings (in square feet) can be modeled b the function S(w) =.5w / 3, where w is the weight of the bird (in pounds). Estimate the weight of a bird with wings having a surface area of.5 square feet. Round our answer to the nearest tenth of a pound. Section Let f ( ) = 3 and g( ) = Determine each of the following. (a) ( f + g)() (b) ( f g )() (c) ( fg)() (d) ( f g)() (e) ( f g)() (f) (g f )() (g) ( f + g )() (h) ( f g )( )

3 6. The graphs of f () and g() are shown at the right. Use the graphs to evaluate each of the following. (a) ( f + g)() (b) ( f g)( ) (c) ( f g)(3) (d) ( fg)( ) (e) ( f g)() (f) (g f )( ) (g) (g g)( ) MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. 3 of 6 = f() = g() 7. Ra recorded a CD of a song he wrote and performs. It cost him $,500 to have the song recorded and it cost him $.00 for each CD he had duplicated. He sold the CD s for $4.00 each. (a) What was Ra s total cost function for recording the CD and having copies made? (b) What was Ra s revenue function for the sale of copies of the CD? (c) What was Ra s profit function for the sale of copies of the CD? (Reminder: Profit = Revenue Cost) (d) If Ra had,000 copies of the CD made and sold them all, what was his profit? Section The table at the right is a complete 0 representation of the function f. f () (a) Is f a one-to-one function? Eplain how ou determined our answer. (b) Does f have an inverse function? (c)evaluate f (3), if possible. 9. If f () = 5 3 4, find the smbolic representation (the formula) for f (). 0. Determine the formula for the inverse function of f () = The graph of = f () is shown on the coordinate sstem at the right. (a) Is f () a one-to-one function? Eplain how ou determined our answer. (b) On the same coordinate sstem, sketch the graph of = f (). (c) What is the relationship between the graphs of = f () and = f ()? ( 4, ) (4,3). For the function f ( ) shown in Problem 3, determine (a) f (0) and (b) f ( ). Section Determine C and a so that the function f () = Ca satisfies the following conditions: f (0) = 40 and f (3) = 5

4 MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. 4 of 6 4. A compan offers a college graduate $50,000 for the first ear of emploment with a guaranteed 6% raise each ear thereafter. Determine a function f (n) that computes the graduate s salar for the n-th ear. 5. The formula for continuousl compounded interest is A = Pe rt, where A is the final value of the account, P is the principal with which the account was started, r is the interest rate (in decimal form), and t is the number of ears. Determine the final value of a savings account started with a deposit of $,000 if the account earns interest at a rate of 6% compounded continuousl for ears. Round our answer to the nearest cent. 6. The formula for interest compounded n times a ear is A = P + r nt, where A is the final value n of the account, P is the principal with which the account was started, r is the interest rate (in decimal form), n is the number of compounding periods in a ear, and t is the number of ears. Determine the final value of a savings account started with a deposit of $5,000 if the account earns interest at a rate of 6% compounded quarterl for 0 ears. Round our answer to the nearest cent. Section Evaluate each of the following epressions eactl: (a) log (b) log 6 0 (c) log00 (d) log Determine the domain for each of the following. Give our answers in interval notation. (a) log( 3) (b) ln( 9) 9. Solve for and round our answer to the three decimal places: (a) e + = 9 (b) 0 3 = Solve for and round our answer to the three decimal places: (a) log + 3 = 8 (b) 3ln( 5) = 6 Section Use Properties of Logarithms to epand each of the following epressions into as man terms as possible. If possible, write our answer without eponents. (a) log 35 4 (b) ln Use Properties of Logarithms to write the following epression as a logarithm of a single epression: (a) log + 4log (b) 4ln ln

MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. 5 of 6 33.

5 MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. 5 of Use the Change of Base Formula to approimate the following logarithm to the nearest thousandth: (a) log 3 00 (b) log 8 3 Answers. (a) 4 5 (b) 3,0 (c) 0, 3 4 (d) = 4 5 (e) = 5 { } (b) ± 4 3,0. (a) 3 { } (b) 5 3,0 3. (a) 3,5 (c) 0, 6 9 (d) = 3 (3) = (c) 0, 3 (d) = 3, = 5 (e) = = 00 00% = % = 0 3 % = 3 3 % 7. ± 6 8. (, 3] (,] (4, ) 9. (, ) (,3) 0. (, 4) [,) [3, ). / pounds 5. (a) 6 + (b) 8 (c) 8 5 (d) (e) (f) 8 7 (g) 8 (h) 6. (a) (b) 0 (c) undefined (d) 4 (e) 3 (f) 0 (g) 4

6 MATH 34 - College Algebra - Review for Test 3 (Thomason) - p. 6 of 6 7. (a) C( ) =500 + (b) R( ) = 4 (c) P( ) = 500 (d) $ (a) Yes, because no value is repeated as an value and no value is repeated as a value. (b) Yes. (c) 9. f () = f () = (a) It is a function because it passes the Vertical Line Test and it is a one-to-one function because it passes the Horizontal Line Test. (b) (c) The graphs of = f ( ) and = f () are smmetric to each other about the line =.. (a) (b) 4 3. f ( ) = f (n) = 50,000(.06) n 5. $4, $9, (a) (b) 4 (c) (d) 3 8. (a), (b) (, 3) (3, ) 9. (a) 3.96 (b) (a) 36.8 (b) (a) log3 + 5log log4 log (b) 5 ln ln 3. (a) log( 4 ) 4 (b) ln 33. (a) 4.9 (b) 5 3

MAT 116 Final Exam Review

MAT 116 Final Exam Review MAT 116 Final Eam Review 1. Determine the equation for the line described, writing the answer in slope-intercept form. The line is parallel to = 8 and passes through ( 1,9). The line is perpendicular to