MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for the eam. Be sure to also review our tet, class notes, class reviews & eams, homework assignments and the final eam review sheet. Directions: Show work for the following problems in the space provided using algebra. Place answers in the blanks. Each problem is worth 6 points. GOOD LUCK! 1. Solve: 4 + 1 = Name: Instructor: Da/Time: 1.. Solve: + 1 = 0 4. 3. Solve: 3 8 < 7. Write our answer using interval notation. Graph our solution on the number line. 3.
4. Solve: + 1 = 0 (Be sure to simplif final answer!) 4. 5. Solve: + + = 5 5 5. 6. Solve: 15 0. State the solution using interval notation, then graph it on the number line. 6.
7. Given + + 4 6 3 = 0, complete the square and write the equation in standard form. Then, state the radius and the center and sketch the graph. 8 Center: (, ) -8 8 Radius: -8 8. The equation H(t) = 16t + 40t + 00 represents the height of a ball thrown upward from the top of a 00-foot tall bridge after t seconds. How long does it take for the ball to hit the water below the bridge? (Hint: H(t) = 0 at the water.) 8. 9. Find the slope and -intercept of : 5 4 = 1. State the intercept as a point. Then graph. 8 slope: -int: -8 8-8
10. Given the following graphs: i) ii) iii) a) Which one(s) would be considered graph(s) of function(s)? 10a. b) Which, if an, is an even function? 10b. c) Which, if an, is a one-to-one function? 10c. 11. Determine the domain: f () = 3 + 5. Epress our answer in interval notation. 11. 1. Given 3 f() = 5 if 0 if > 0 a) Find f(9) 1a. b) Find f( 1) 1b.
13. The graph of a function f is shown in the figure below. Use the graph to answer the following questions: > a) State the domain using interval notation 13a. b) State the range using interval notation 13b. c) Find f(5) 13c. 14. Graph g() = 9 on our calculator in the standard window. a) Sketch the graph that ou see: b) State an -intervals over which the graph is increasing or decreasing. Increasing: Decreasing: 15. Given f() = 3 and g() = + 5, compute (g f)( ) 15.
For #16 & #17, describe, in words, how each of the following functions can be obtained from the graph of a common algebraic function (i.e. shifts right, shifts up 5, stretches horizontall, etc.). Then sketch the graph. 1 16. f() = 3 + Description: 10 10 17. h () = + 5 Description: 10 10 18. Given: f() = ( + 3), state the verte and -intercept (as points), state the ais of smmetr (as an equation), and graph. Verte: Y-Intercept: Ais of Smmetr: 10 10
19. A gardener wants to put fencing around a rectangular garden that is adjacent to a barn(see diagram). Fencing is not needed along the barn side. If the gardener has 56 feet of fencing, determine the dimensions of the garden that will maimize the area. What is the maimum area? Let be the width as shown. BARN Garden Dimensions: Ma Area: 0. Find the - and -intercepts of: 3 1 R() = Be sure to state our answer as points. -intercept: -intercept: 1. Determine the equations of the horizontal and vertical asmptotes of R() = 3 1 vertical asmptote: horizontal asmptote:. Using the information from #0 & #1, graph 3 1 R() =. 10 10
3 3. Given f() = and g () =, find f o g 3 3. 4. Given f() = 5, find f 1 () 4. 5. Solve the following sstem of equations: 5 + 6 = 3 3 = 10 5.
6. Graph the solution set of this sstem of inequalities: + 4 8 7 + 4 8 0 0 10 10 7. Graph f() = 3 10 10 8. Determine the domain and range of f() = log4 ( + 3). Use interval or inequalit notation. Domain: Range: 9. A population of bacteria decas, when treated with disinfectant, according to the model 0.65t A = 100 e, where t is time in minutes. How man bacteria are present after 10 minutes? Round to the nearest whole number. 9.
30. a) Evaluate without using our calculator: log 6 ( 6) 30a. b) Evaluate using our calculator, rounding to 3 decimal places: log 8 ( 43) 5 30b. 31. Solve: e = 10 Epress our answer in terms of natural logarithms, then use our calculator to approimate the solution to the nearest thousandth. 3. Write as a single logarithm: log + log 3 log z 4 4 4 31. 33. Solve: log 3 ( + 7) = 3 3. 33.
34. Use our calculator to solve: log( + ) = + 8. Sketch the graph ou see and round our solution to decimal places. 34.
ANSWER KEY TO MAC 1105 PRACTICE FINAL EXAM 1. = 7. = ±i, ± 3 1 3., 5 3 ( ) 1 3 5 10. a) ii, iii b) iii c) ii 11. 5, ) 3 1. a) f(9) = 1 b) f( 1) = 4 13. a) [ 4, ) b) [ 1, ) c) f(5) = 4. = 1± 3 14. a) 5. = 4, 3 6. (, 3] [ 5, ) ] [ 3 5 7. Center: (, 3); r = 4 b) Increasing: ( 3, 0), (3, ) Decreasing: (, 3), (0, 3) 15. (f g)( ) = 9 8 16. Shrinks verticall, shifts up -8 8-8 8. 5 seconds 9. m = 4 5, -int: (0, 3) 17. Moves left 5, reflects across the -ais
18. Verte: ( 3, ) -int: (0, 7) Ais of Sm: = 3 7. 19. Dimensions: 14 ft 8 ft Ma Area: 39 sq-ft 8. Domain: ( 3, ) Range: (, ) 9. 3 bacteria 1 0. -int:, 0 3 -int: 1 1 0, 30. a) b).64 1. v.a.: = h.a.: = 3. 31. 5 ln10 = 1. 349 3. log 4 3 z 33. = 10 34. 3. f o g = 4. f 1 () = 5 4 5., 3 3.6 6.