MATH College Algebra Review for Test 3

Transcription

1 MATH College Algebra Review for Test Section The graph of a rd, 4 th, or 5 th degree polnomial f () with integer zeros is shown at the right. Determine the factored form of f ().. Solve eactl for : = 0. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible.. Solve eactl for : = 4 1. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an comple solutions in standard form. 4. Solve eactl for : 6 =10 1. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an comple solutions in standard form. 5. Find the zeros of f () = given that 7 is a zero. Section The graph of a 5 th degree polnomial f () is shown at the right. (a) How man different real zeros does f () have? (b) How man different imaginar zeros does f () have?

2 MATH College Algebra - Review for Test (Thomason) - p. of 6 7. Find the completel factored form of a polnomial f () with real coefficients that satisfies the following conditions: Degree ; a = ; zeros include and 1 i 8. Find the completel factored form of a polnomial f () with real coefficients that satisfies the following conditions: Degree 4; a n = 1; zeros include 0,, and i 9. (a) Find all the zeros of f ( ) = (b) Write f () in completel factored form. 10. (a) Find all the zeros of f ( ) = 4 +. (b) Write f () in completel factored form. 11. (a) Find all the zeros of f ( ) = (b) Write f () in completel factored form. Section 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. 1. 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 ( ) = 15. (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. 15. Use transformations of the memorized graph for = 1 to graph = 1 + on the coordinate sstem at the right.

3 MATH College Algebra - Review for Test (Thomason) - p. of Use transformations of the memorized graph for = 1 to graph = 1 4 on the coordinate sstem ( + ) at the right. 17. 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 Solve for and give our solution in interval notation: +15 < 19. Solve for and give our solution in interval notation: ( + 4)( )( 5) 0 0. Solve for : = 5 1. 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.) 1. Solve for and give our answer in interval notation: 1 < 0. Solve for and give our answer in interval notation:

4 MATH College Algebra - Review for Test (Thomason) - p. 4 of 6 Section Use laws of eponents to write the following as a single power of : 4 5. Solve for : 4 8 = 6. Solve for : = 7. Suppose that the surface area S of a bird's wings (in square feet) can be modeled b the function S(w) =1.5w /, 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 Determine C and a so that the function f () = Ca satisfies the following conditions: f (0) = 40 and f () = 5 9. 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. 0. 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 1 ears. Round our answer to the nearest cent. 1. The formula for interest compounded n times a ear is A = P 1+ r, 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 10 ears. Round our answer to the nearest cent. Section 5.4. Evaluate each of the following epressions eactl: (a) log 1 (b) log (c) log100 (d) log 9. Determine the domain for each of the following. Give our answers in interval notation. (a) log( ) (b) ln( 9) 4. Solve for and round our answer to the three decimal places: (a) e + = 9 (b) 10 = 7 nt

5 MATH College Algebra - Review for Test (Thomason) - p. 5 of 6 5. Solve for and round our answer to the three decimal places: (a) log + = 8 (b) ln( 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 5 4 (b) ln 5 7. Use Properties of Logarithms to write the following epression as a logarithm of a single epression: (a) log + 4log (b) 4ln ln 8. Use the Change of Base Formula to approimate the following logarithm to the nearest thousandth: (a) log 100 (b) log 8 Answers 1. f ( ) = 1 ( +1) ( )( 4). ±, 5 7. ± i 4., , 1 ± 7 i 6. (a) (b) 7. f ( ) = ( )[ (1 i)][ (1+ i)] 8. f ( ) = ( )( i)( + i) 9. (a), ±i (b) f ( ) = ( )( i)( + i) 10. (a) 0, ±i (b) f ( ) = 4( i )( + i ) ( ) ( ) 11. (a) 0, 1 ± i (b) f ( ) = 1 i 1+ i 1. (a) (a) { } (b) ± 4,0 { } (b) 5,0 14. (a),5 (b),0 (c) 0, 4 (d) = 4 5 (e) = 5 (c) 0, 16 9 (d) = () = 9 (c) 0, 1 (d) =, = 5 (e) = 0

6 MATH College Algebra - Review for Test (Thomason) - p. 6 of = % = 0 0 % = 10 % = 1 % 18. (,0) (5, ) 19. [ 4,] {5} 0. ± 6 1. (, ] (,] (4, ). (, 1) (1,). (, 4) [,1) [, ) 4. 1/ pounds 8. f ( ) = f (n) = 50,000(1.06) n 1 0. $4, $9, (a) 1 (b) 4 (c) (d). (a), (b) (, ) (, ) 4. (a).96 (b) (a) 16.8 (b) (a) log + 5log log4 log (b) 5 ln + 5 ln 7. (a) log( 4 ) 4 (b) ln 8. (a) 4.19 (b) 1.667