Final Exam REVIEW- Intermediate Algebra

Transcription

1 Final Eam REVIEW- Intermediate Algebra Solve the inequalit. Write the solution set in interval notation and graph the solution set. 1) 7z - 7 6z - 7 1) Solve the compound inequalit. Graph the solution set and write it in interval notation. 2) 9-6 < 3 or ) Solve the absolute value equation. 3) = ) Solve the equation for the specified variable. 4) 1 p + 1 q = 1 f for f 4) ) P = A 1 + rt for r ) Solve the equation. 6) = ) Graph the union or intersection, as indicated. 7) The intersection of -2 and 7)

2 8) The union of + > 2 or ) List the elements of the set. 9) If A = { is an odd integer} and B = {-11, -9, -8, -6}, list the elements of A B. 9) Find the domain of the rational function in interval notation. ) f() = ) Write the inequalit. 11) Write -8 8 as an inequalit containing absolute value. 11) Graph the union or intersection, as indicated. 12) The intersection of + - and ) ) The intersection of - < -2 and > -3 13)

3 Graph the inequalit. 14) - > -3 14) Solve the equation. 1) = ) Use the square root propert to solve the quadratic equation. 16) (2 + 3)2 = 2 16) Factor the polnomial completel. 17) ) 18) ) 19) ) Solve the absolute value equation. 20) = 12 20) Solve the inequalit. Graph the solution. Write the solution in interval notation. 21) ) 22) ) 23) > -4 23) Solve the compound inequalit. Graph the solution. Write the solution in interval notation. 24) 9 < 36 and + 9 > 7 24) 3

4 Solve the inequalit. Graph the solution. Write the solution in interval notation. 2) 6k + 8 < -3 2) Solve the inequalit. Graph the solution. 26) + 8 > ( + 11) 26) Solve the compound inequalit. Graph the solution. Write the solution in interval notation. 27) -14-2c - 2 < -8 27) Write the function in the form f() = a( - h)2 + k. 28) f() = ) Solve the equation b completing the square. 29) = 0 29) 30) = 0 30) Use the discriminant to determine the number and tpe of solutions of the equation. 31) = 0 31) 32) 72 = ) Use the quadratic formula to solve the equation. 33) 22 + = ) 34) ( + 6) = 6 34) For the given functions f and g, find the requested function. 3) f() = 3 ; g() = 6 - Find (f - g)(). 3) 36) f() = 94; g() = 32 Find f (). 36) g 37) f() = ; g() = - 3 Find f (). 37) g Find the domain of the rational function in interval notation ) f() = ) 4

5 Divide using snthetic division. 39) ) Use the Remainder Theorem (and snthetic division) to evaluate the function at the given c. 40) P() = ; 2 40) Use the properties of eponents to simplif the epression. 41) /9 (3/9-92/9) 41) Simplif. 42) ) Simplif. 43) ) Simplif. 44) ) Simplif. 4) ) Simplif. 46) ) Perform the indicated operation ) ) Solve the equation. 48) 22/3-31/3-20 = 0 48) Solve. 49) (3-6)2 + 9(3-6) = ) 0) ( - 2)2 = -18 0)

6 Solve the equation. 1) 4 = 81 1) 2) 3-8 = 6-2) Add or subtract. Assume all variables represent positive real numbers. 3) ) Rationalize the denominator and simplif. Assume that all variables represent positive real numbers. 9 4) ) ) ) Perform the indicated operation. Write the result in the form a + bi. 6) 1-7i 4 + i 6) Solve the problem. 7) A painter can finish painting a room in hours while her assistant takes 7 hours to finish the same job. How long would it take them to complete the job if the work together? 7) For the given functions f and g, find the composition. 8) f() = + 9; g() = 8-13 Find: (g f)() 8) Solve the problem. 9) An arrow is fired into the air with an initial velocit of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given b the function h(t) = -16t2 + 96t. Find the maimum height of the arrow. 60) Jerod can run miles per hour on level ground on a still da. One wind da, he runs miles with the wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the wind? 9) 60) 61) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. 61) For the given functions f and g, find the composition. 62) f() = 3 + 8; g() = -2 Find: (g f)() 62) 6

7 Graph the function. State the Domain and Range. 63) + 1 if 0 f() = 1-4 if > 0 Domain: Range: 4 63) - - Solve the problem. 64) Find the midpoint of the line segment whose endpoints are 3 2, 3 4, - 4, ) 6) Find the distance between the points (-, 1) and (7, 7). 6) Find the indicated value. 66) Use the graph to determine f(3). 66) - - 7

8 Graph the function. State the Domain and Range. 67) f() = + if < if > 2 Domain: Range: 67) Graph the function. State the Domain and Range. 68) f() = 1 if < -6-6 if -6 68) Domain: Range: Sketch the graph of the quadratic function. Give the verte and the ais of smmetr. 69) f() = ) - - smmetr: Verte: Ais of 8

9 Graph the function. Identif the Domain and Range. 70) f() = ) - - Domain: Range: Sketch the graph of the given function. Give the verte and ais of smmetr. 71) h() = -( - 4) ) Verte: Ais of smmetr: 9

10 Graph the function. Identif the Domain and Range. 72) f() = ) - - Domain: Range: Sketch the graph the function. Identif the domain and range. 73) f() = ) - - Domain: Range: Sketch the graph of the function. 74) h() = )

11 7) g() = ) - - Solve the inequalit. Graph the solution set and write the solution set in interval notation. 76) ) 77) > 0 77) 78) > 0 78) Graph the function. Determine the verte, the ais of smmetr, and the -intercept. 79) f() = -3( - 2) ) Verte: Ais of smmetr: -int 11

12 Sketch the graph of the quadratic function. Give the verte and ais of smmetr. 80) f() = 1 ( - 4) ) Verte: Ais of smmetr: 12

13 Answer Ke Testname: FINAL REVIEW INTERMEDIATE ALGEBRA 1) [0, ) 12) ) (-, 1) [3, ) ) - 1 9, - - 4) f = pq p + q ) r = A - P Pt 6) 7) 13) ) 8) ) {-11, -9} ) (-, ) 11) 8-1) -3, - 3, 3 16) 1, -4 17) 2(4 + 3)( ) 18) 3( + 7)( - 7) 19) (6 + 1)2 2 20), ) [3, 7]

14 Answer Ke Testname: FINAL REVIEW INTERMEDIATE ALGEBRA 22) (-, ) 23) (-, ) ) (-2, 4) 2) 26) ) (3, 6] ) f() = ) 30) , i i 19, ) one real solution 32) two comple but not real solutions 33) , ) -3-1, ) (f - g)() = f 36) g () = 3 2, where 0 f 37) g () = - 3, where 3 38) (-,0) (0,3) (3,7) (7, ) 1 39) ) P(2) = 13 41) 8/9-97/9 42) ) ) ) ) ) 48) 64, ) 2 3, 1 3 0) i, i 1) -3, 3, -3i, 3i 2) { 4 } 3) ) ) ) i 7) hours 8) ) 144 ft 60) mph 61) 2 thousand automobiles 62) ) Domain: (-, ); Range: (-, ) 64) - 4, 1 4 6) 6 units 66) f(3) =

15 Answer Ke Testname: FINAL REVIEW INTERMEDIATE ALGEBRA 67) Domain: (-,2) (2, ); Range: (-,7) (2, 7) 71) verte: (4,3); ais = 4 (2, 3) ) Domain: (-, ); Range: {-6,1} - 72) Domain [-4, ); Range [-7, ) ) verte: (2, 1); ais = 2-73) Domain (-, ); Range (-,0] ) Domain [1, ); Range (-,0] 74)

16 Answer Ke Testname: FINAL REVIEW INTERMEDIATE ALGEBRA 7) 80) verte: (4, 1); ais: = ) (-, -3] [1, ) ) -, - 4 4, ) - 7 6, ) verte: (2, 3); ais: = 2; -int: (0,-9) (2, 3) (0, -9) - 16