Name Block Date Honors Algebra : Semester 1 Review NON-CALCULATOR 6-5 1. Given the functions f ( ) 5 11 1, g( ) 6 ( f h)( ) b) ( g f )( ), and h ( ) 4, find each function. g c) (g h)( ) d) ( ) f -1, 4-7, -8. Let k( ) be the indicated transformation of h( ). Write the rule and equation for ( ) Vertical stretch b a factor of 5 and a translation left 1 unit and down 9 units. k.. Let g ( ) be the indicated transformation of f( ). Write the rule and equation for g ( ). A horizontal compression b a factor of ¼, a reflection across the -ais, and a translation up 7 units. 4. Let h ( ) be the indicated transformation of k( ). Write the rule and equation for h ( ). A vertical stretch b a factor of 6, a reflection across the -ais, and a translation right units and down 8 units. 5. Let f( ) be the indicated transformation of g( ) 4. Write the rule and equation for ( ) f. A vertical compression b a factor of 1/9, a horizontal stretch b a factor of 5, and a translation left 7 units and up units.
For 6 9, identif the parent function, describe the transformation, use a table to graph the transformed function, and state the domain, range and asmptote, if an. 6. h 1 7 Parent Function: Description: Domain: Range: 7. 1 g ( ) 4 Parent Function: Description: Domain: Range: Asmptote: 1 8. k ( ) ( 4) 5 Parent Function: Description: Domain: Range: 1 ( ) 6 Parent Function: 9. f Description: Domain: Range:
4-, 6-6 10. Determine whether the inverse of each relation is a function. Eplain our reasoning. b) 11. Graph g 6, then write and graph the inverse. 4 1. Given the function h ( ) : Graph h ( ) and h 1 ( ). b) State the domain and range of each function. h ( ): : h 1 ( ) D: D: R: R: c) Find the equation of the inverse function.
1-7 1. Use the graph to find the solution(s) to the sstem. b) 4-1 14. State whether each function shows growth or deca. Eplain our reasoning. Then, sketch and label a graph of the function. 1 f( ) () b) g ( ) 4(.19) 4-15. Write each eponential equation in logarithmic form. 5 15 b) 1 7 18 16. Write each logarithmic equation in eponential form. 1 1 log8 b) log4 7 64 4-4, 4-6 17. Use properties of logarithms to simplif the following epressions. log 18 b) log(61) 10 1 log 81 c) d) ln e (9) 5 1 e) log4 64 f) log 8 1 g) log 0 log 50 h) log 8 100 log 8 5 i) log510 log5 log58
4-5 18. Solve each equation algebraicall. 5 15 b) 16 4 5 7 c) log (8 1) 4 d) log 5 log 4 6-5 19. Solve each equation algebraicall. 98 0 b) 4 00 0 0. Solve each equation b completing the square. f ( ) 17 b) g ( ) 4-6 1. Find the zeros of each function using the quadratic formula. h( ) 8 b) k ( ) 9 5
. Determine what tpe and how man solutions there are for graph of the function. 4 8. Sketch a possible -9. Plot 5 i in the comple plane. 4. Calculate 6i 5. Write the comple conjugate of 1 7i. 6. Simplif each epression. Write our result in the form a bi. ( 8 i) (9 i) b) (6 i)( i) c) i d) 8 5 (7 ) i 5 i e) 119 6i f) 7i i 4 85
- 7. Divide: (4 8 9 10) ( 1) 8. Divide: (5 18 7) ( ) -4 9. Is ( ) a factor of P( ) 9 9 10? Eplain our reasoning. 0. Factor each polnomial epression completel. 4w 8w w b) 6 8 7 c) 5 4 c 14c 18c 16c d) 10 n 50 n
-5 1. Solve h( ) 6 6 16 b factoring, and state the multiplicities. -6. Write the simplest polnomial function given the roots -7, i,. Leave our answer in factored form. -7. Given the function f 1 : Identif the degree and leading coefficient. b) Describe the end behavior of the graph. c) Find the zeros of the function. d) Find the -intercept of the function. e) Sketch a graph of the function based on the above information. 4. Given the function 4 g 51 48 : Identif the degree and leading coefficient. b) Describe the end behavior of the graph. c) Find the zeros of the function. d) Find the -intercept of the function. e) Sketch a graph of the function based on the above information.
CALCULATOR ALLOWED 6-6 5. The approimate time t in seconds it takes an object to fall a distance of d feet is given b d t. 16 Find the inverse of the function. b) Eplain what the inverse represents. c) Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during that time? -7 6. For each equation, sketch a graph of the function and identif the following ke features: i) state the domain and range, ii) state the absolute maimum and minimum, iii) state the local maimum and minimum, iv) write the equation of an asmptotes, and v) state the end behavior. f b) ( ) 4() g 7 5 4-1 7. Mr. Mahew bought his truck for $,000. Its value depreciates 8.5% each ear. Write an equation to represent the value of Mr. Mahew s truck as a function of time. b) How much will his truck be worth after ears? c) How man ears will it take for the truck to be worth $8000? 8. If a savings account earns.75% annual interest, how much will a deposit of $4700 be worth in 6 ears if the interest is compounded quarterl?
4-6 9. How much is an initial investment of $10,500 worth after 5 ears when the interest of 7% is compounded continuousl? 40. A paleontologist uncovers a fossil of a saber-toothed cat in California b the analsis of carbon-14. Carbon-14 has a half-life of about 570 ears. Use the function N() t N0e kt to model this situation. Find the deca constant. b) Determine the amount of the initial 8 grams of carbon-14 that remains after 9000 ears. c) How long will it take for 8 grams to deca to grams? 4-4 41. Evaluate each logarithm to the nearest thousandth. log 6 9 b) log7 8 4. The Richter magnitude of an earthquake, M, is related to the energ released in ergs, E, b the E formula M log 11.8 10. 19 In August 011, an earthquake struck Colorado releasing approimatel 5.6 10 ergs of energ. What was the magnitude of this earthquake? b) Find the inverse of the original equation. c) How much energ was released b the 9.0 earthquake that struck off the coast of Japan in March of 011?
1-7 4. Solve each sstem of equations b graphing. Include a sketch our graph. 10 1 76 4 b) 1 5 ( ) 6 14 4-5 44. Solve each equation and inequalit graphicall. Include a sketch of our graph. 7 5 0 b) log(8 0) 1 c) 49 5 d) ln 7-4 45. Use a graph to factor polnomial in factored form. f ( ) 6 40 19. Verif all factors algebraicall. Write the -5, -6 46. Identif the roots of each equation. Verif all roots algebraicall. 4 5 6 6 0 0
46. Identif the roots of each equation. Verif all roots algebraicall. b) 1116 0 c) 4 7 108 0 47. Stephen has a set of plans to make a wooden bo. He wants to reduce the volume of the bo to 105 cubic inches. To accomplish the reduction in volume, he would like to reduce the length of each dimension in the plans b the same amount. The plans call for the bo to be 10 inches b 8 inches b 6 inches. Write and solve a polnomial equation to determine how much length Stephen should take from each dimension. -9, 4-8 48. A small group of farmers joined together to grow and sell wheat in 1985. The table shows how their production of wheat increased over 0 ears. Years after 1985 6 10 1 16 0 Wheat Produced (Tons) 70 105 150 10 40 580 Find an eponential function to model this data. b) Use the model to predict what their wheat production will be in the ear 015. c) Use the model to predict when their wheat production eceeded 700 tons.
49. The table shows the U.S. production of tobacco from 1997 to 00. Years after 1996 1 4 5 6 Tobacco ( 100,000 lbs) 1787 1480 19 105 99 890 Find a logarithmic function to model this data. b) Use the model to predict when tobacco production fell below 50,000,000 (500 100,000) lbs. c) Use the model to predict the tobacco production in the ear 005. 50. A variet of spruce trees called No. 1 Common Spruce are often used as support columns in buildings. The maimum load allowance for each column depends on the height of the spruce column. The table shows some of this data. Height of the Column (ft) 4 5 6 7 8 Maimum Load (lb) 780 7100 6650 590 4940 Use finite differences to determine the degree of the polnomial that best models the data. b) Write the polnomial function for the data. c) Use the model to predict the load allowed for a 6.5 foot spruce column. d) What is the maimum load a Common Spruce of an height can hold? e) What is the height of the spruce column at that maimum load? 51. The table shows the number of hummingbirds who visited Mr. Hunt s birdfeeder between 7:00 a.m. and 8:00 a.m. from Januar through June 011. Number of Months 1 4 5 6 Number of Birds 8 18 6 65 108 Use finite differences to determine the degree of the polnomial that best models the data. b) Write the polnomial function for the data. c) Use the model to predict the number of hummingbirds in November.