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1 Workbook To jump to a location in this book 1. Click a bookmark on the left. To print a part of the book 1. Click the Print button.. When the Print window opens, tpe in a range of pages to print. The page numbers are displaed in the bar at the bottom of the document. In the eample below, 1 of 151 means that the current page is page 1 in a file of 151 pages.

2 1.1 Tables and Graphs of Linear Equations State whether each equation is linear Graph each linear equation Determine whether each table represents a linear relationship between and. If so, write the net ordered pair that would appear in the table Algebra Workbook 1

3 1. Slopes and Intercepts Write the equation in slope-intercept form for the line that has the indicated slope, m, and -intercept, b. m, b m 5, b 5 m 3, b 1 m 1 6, b m, b 3 m 1, b Find the slope of the line containing the indicated points. 7. (3, 0) and ( 3,) 8. ( 1, 1 5 ) and ( 3, 3 ) 9. (, 6) and (1, 5) 10. ( 1, 5 ) and (, ) Identif the slope, m, and the -intercept, b, for each line Write an equation in slope-intercept form for each line (0, 3) 8 (6, 8) 6 O 6 8 (0, 3) (8, 3) Workbook Algebra

4 1.3 Linear Equations in Two Variables Write an equation for the line containing the indicated points. 1. (, ) and (3, 5). ( 1, 3) and (3, 1) ( 1, 3 ) 3. (3, 1) and. (, 0) and ( 6, ) 5. ( 1, ) and (, 5) 6. ( 1 and (, 1, 3 ) ) Write an equation in slope-intercept form for the line that has the indicated slope, m, and contains the given point. 7. m 1 and (3, 3) 8. m 1 and (,6) 9. m 3 and (, ) 10. m and (, 3) 11. m and (, 3) 1. m 1 and (8, 6) Write an equation in slope-intercept form for the line that contains the given point and is parallel to the given line. 13. (1, ); 3 1. (, 3); 15. (, ); ( 6, 3); 17. (, 1); (3, ); (, ); (1, 1); 3 1. (, ); 1. 3 (1, 0); 3 Write an equation in slope-intercept form for the line that contains the given point and is perpendicular to the given line. 3. (, ); 1. (6, ); (6, 7); 5 6. (, 5); 7. (3, 11 ; 8. ) 6 (3, 5); 1 9. (1, ; 3 ) (1, ); (3, 1); ( 1, 7 ); 3 Algebra Workbook 3

5 1. Direct Variation and Proportion In Eercises 1 8, varies directl as. Find the constant of variation, and write an equation of direct variation that relates the two variables ,for. 7,for 3 3.,for 3. 3.,for ,for ,for 6 7.,for ,for Solve each proportion for the variable. Check our answers z Determine whether the values in each table represent a direct variation. If so, write an equation for the variation. If not, eplain wh not z 7 z Workbook Algebra

6 1.5 Scatter Plots and Least-Squares Lines Create a scatter plot of the data in the table below. Describe the correlation. Then find an equation for the least-squares line A baseball plaer has plaed baseball for several ears. The following table shows his batting average for each ear over a 10-ear period In Eercises 6, refer to the table above.. Enter the data in a graphics calculator, and find the equation of the least-squares line. 5. Find the correlation coefficient, r,to the nearest tenth. 6. Use the least-squares line to predict the baseball plaer s batting average in Algebra Workbook 5

7 1.6 Introduction to Solving Equations Solve each equation. ( 1) ( 3) (3 19) (3 ) ( ) ( 3) ( ) ( 3) ( ) 3 5( 1) ( 3) ( ) 5 9 ( 3) 5( 3) 7 ( 3) 5( 0.5) 1.5( 3) Solve each literal equation for the indicated variable ( ) 3 (3 6) 1 L W D V, for W C πr, for r V 1 P 1 V P, for P 1 q q p D Q, for q p T T o a(z z 0 ), for a 3( ) ( 3) 3 8. A (a b)h, for h 6 Workbook Algebra

8 1.7 Introduction to Solving Inequalities Write an inequalit that describes each graph Solve each inequalit, and graph the solution on a number line ( 3) ( ) 7. Graph the solution of each compound inequalit on a number line ( ) or 6 t and t Algebra Workbook 7

9 1.8 Solving Absolute-Value Equations and Inequalities Solve each equation. Graph the solution on a number line and Solve each inequalit. Graph the solution on a number line Workbook Algebra

10 .1 Operations With Numbers Classif each number in as man was as possible State the propert that is illustrated in each statement. Assume that all variables represent real numbers ( 75) (33 18) ( 33) k k 5 1,where k ( 91) 1 1(91) Evaluate each epression b using the order of operations ( 11) (13 7) 5. (77 50) (13 ) Algebra Workbook 9

11 . Properties of Eponents Evaluate each epression (15 1 ) ( 3) 3.. ( 17) 1 ( 3 ( 1 5 ) ( ) 0 5 ) ( 1 ) 5 ( 1 ) 73 Simplif each epression, assuming that no variable equals zero. Write our answer with positive eponents. d 3 d w 3 z w z k 11 k z z ( 7) 5 1 z z (3 3 5 ) 1.. ( 7 ) w 1 w 1 w 9 3. (5a b 3 ). ( wz ) 5. ( a b 3 ) 6. ( w6 k ) 3 7. ( 8. ( p 3z mp 3 ) z ) 1 9. ( ) ( 3 ) 8 () 3 3 ( a3bc6 ) 10 Workbook Algebra

12 .3 Introduction to Functions In Eercises 1 8, state whether each relation represents a function O O O {(1, 5), (0.5, 8), (0, 3)} {(3, ), (16, 7), (16, )} State the domain and range of each function ( 1, 3), (0, 1), ( 1, 3 ), ( 3, 7 ) {(.5, 6), (3, 1.5), (6.5, 5), (1, 10.5)} {(, 1), (0, 8), (1, 9)(5, 33)} Evaluate each function for the given values of. 13. f() 0,for and 8 1. f() 5,for 3 and 5 O 15. f() 1 3,for 7 and f() 3,for 11 and 17. f() 3,for 0.5 and 0 Algebra Workbook 11

13 . Operations With Functions Find f g and f g f Find f g and g. State an domain restrictions f() 7 5; g() 13 f() 1 5; g() 13 f() 1 3 9; g() 7 7 f() 9 6; g() 1 f() 35 5; g() 5 f() 5; g() 3 17 f() 16; g() 16 Let f() and g() 10. Find each new function, and state an domain restrictions f g g f Find f g and g f f g g f f() 3 ; g() 1 3 ( ) f() ; g() 1 f() 1; g() Let f() 11, g() 5, and h() ( ). Evaluate each composite function. (f g)( 1) (h f)( ) f g f g (h g)() (g h)() (g f)(0) (f h)(5) 3. (f g)(0). (h h)( 1) 5. (f f)() 1 Workbook Algebra

14 .5 Inverses of Functions Find the inverse of each relation. State whether the relation is a function and whether its inverse is a function {( 1, 16), (0, 6), (, 1)} {(7, ), (6, 3), (7, ), (6, 5)} {(, 16), ( 1, 1), (1, 1), (, 16)} {( 5, 7), ( 3, 7), ( 1, 7), (1, 7)} {( 5, ), ( 3, 9), (1, 1), (7, 13)} For each function, find the equation of its inverse. Then use composition to verif that the equation ou wrote is the inverse. 6. f() 1 7. h() 1 3 ( 1) 3 g() f() 1 (.5) g() 8( ) Graph each function, and use the horizontal-line test to determine whether the inverse is a function. f() g() 3 1 h() 8 h() 3 Algebra Workbook 13

15 .6 Special Functions Graph each function. 1 if 0 g() 1 if 0 f() if if h() [] Write the piecewise function represented b each graph Evaluate. O O 7. [ 9.3] [.].5 O [.5] [ 6.3] [.9] 1 Workbook Algebra

16 .7 A Preview of Transformations Identif each transformation from the parent function f() to g g() ( 7.5) g() 7.5 g() (5) g() g() 1 6 g() 1( 7) Identif each transformation from the parent function f() to g g() 1 g() 17 g() 1 g() g() 3 g() 1 8 Write the function for each graph described below. 13. the graph of f() 3 reflected across the -ais 1. the graph of f() 5 translated 7 units to the left 15. the graph of f() stretched horizontall b a factor of the graph of f() compressed verticall b a factor of the graph of f() 3 9 reflected across the -ais 18. the graph of f() 3 translated 33 units down Algebra Workbook 15

17 3.1 Solving Sstems b Graphing or Substitution Graph and classif each sstem. Then find the solution from the graph O O O Use substitution to solve each sstem of equations. Check our solution O O O Workbook Algebra

18 3. Solving Sstems b Elimination Use elimination to solve each sstem of equations. Check our solution Use an method to solve each sstem of linear equations. Check our solution Algebra Workbook 17

19 3.3 Linear Inequalities in Two Variables Graph each linear inequalit O O O O O O 7. Sheila earns a basic wage of $8 per hour. Under certain conditions, she is paid $1 per hour. The most that she can earn in one week is $00. a. Write an inequalit that describes her total weekl wages for hours at $8 per hour and for hours at $1 per hour. b. Graph the inequalit on the grid at right. c. What is the maimum number of hours that Sheila can work for $8 per hour? for $1 per hour? O Workbook Algebra

20 3. Sstems of Linear Inequalities Graph each sstem of linear inequalities O O O Write the sstem of inequalities whose solution is graphed (, ) (, ) (, ) (, 5) (, 1) (, 3) (, 1) O O 7. During the summer, Ran works 30 hours or less per week mowing lawns and delivering newspapers. He earns $6 per hour mowing lawns and $7 per hour delivering papers. Ran would like to earn at least $16 per week. Let be the number of hours mowing, and let be the number of hours delivering papers. Write a sstem of inequalities to represent the possible hours and jobs that Ran can work, and graph this sstem at right. (, ) O O Algebra Workbook 19

21 3.5 Linear Programming Graph the feasible region for each set of constraints , 0 0, , O 6 8 O 6 8 O 6 8 The feasible region for a set of constraints has vertices at (,0), (10, 1), (8, 5), and (0, ). Given this feasible region, find the maimum and minimum values of each objective function. F maimum: maimum: maimum: minimum: minimum: minimum: Find the maimum and minimum values, if the eist, of each objective function for the given constraints. P 5 Constraints: G 0 10 Constraints: E E 8 Constraints: F 1 5 Constraints: M 3 0 Workbook Algebra

22 3.6 Parametric Equations Graph each pair of parametric equations for the interval 3 t 3. (t) 1 (t) 6 t (t) t. 3. t 5 (t) t 1 (t) 1 t 1 (t) t 3 O 6 O O Write each pair of parametric equations as a single equation in and. (t) t 1 (t) 1 (t) t. 5. t 6. (t) t 8 (t) 6 t (t) 3t (t) 10 t (t) t An airplane is ascending at a constant rate. Its altitude changes at a rate of 1 feet per second. Its horizontal speed is 150 feet per second. 10. a. Write parametric equations that represent the plane s flight path. b. Graph the equations for the interval 0 t 30. Use the grid at right. 11. a. How long will it take the plane to reach an altitude of 300 ft? b. How far will the plane travel horizontall in that time? (t) 3 1t (t) t 3 (t) 3t (t) t O Algebra Workbook 1

23 .1 Using Matrices to Represent Data In Eercises 1 13, let,,, 0 7 D E F and. 3 3 G Give the dimensions of each matri. 1. D. E 3. F. G Find the indicated matri. F D G E D E E D F G G Matri M at right represents the number of medals won b athletes from the United States, German, and Russia in the 1996 Summer Olmpic Games. 1. What are the dimensions of matri M? 15. Find the total number of medals won b the United States. 16. Find the total number of gold medals won b the three nations. 17. Describe the data in location m 3. F G United States German Russia 18. In the 1996 Summer Olmpic Games, athletes from China won 16 gold medals, silver medals, and 1 bronze medals. Write a new matri, M, that includes medals for all four countries. D 3E Gold Silver Bronze Workbook Algebra

24 . Matri Multiplication Find each product, if it eists [ 0 ] [ 1] Matri T,, represents triangle XYZ, which 0 is graphed at right. 10. Find the coordinates of the vertices of the image, triangle X Y Z, which is formed b multipling matri T b the transformation matri Sketch the image, triangle X Y Z, on the grid at right above. 1. Describe the transformation. 6 Y X 6 O 6 6 Z Algebra Workbook 3

25 .3 The Inverse of a Matri Determine whether each pair of matrices are inverses of each other , 3,, , , Find the determinant and the inverse of each matri, if it eists , Find the inverse matri, if it eists. If the inverse matri does not eist, write no inverse Workbook Algebra

26 . Solving Sstems With Matri Equations Write the matri equation that represents each sstem. 3 z 19 3z 1 z 7 5 z 13 z 1 8 3z z 6 3 z 3 1 Write the sstem of equations represented b each matri equation z z Write the matri equation that represents each sstem, and solve the sstem, if possible, b using a matri equation z 1 8 7z 5 9z z z z 3 3 z 1 3 z 15 z z 5 z z z z z 1 1 5z 8 Algebra Workbook 5

27 .5 Using Matri Row Operations Write the augmented matri for each sstem of equations. 5 z 3z 7 9 z z 6 z 7 8 3z z 1 3 3z 6 7 3z 8 Find the reduced row-echelon form of each matri. 1 0 M M M M 1 0 M 0 M M M M M M M M 1 M M M M M Solve each sstem of equations b using the row-reduction method z 1 z 1 3 z 7 5 3z 11 3 z z 3z 1 3 5z 3 z 6 3 z 16 3z z z z 9 3 z 19 3z 15 3 z 13 6 Workbook Algebra

28 5.1 Introduction to Quadratic Functions Show that each function is a quadratic function b writing it in the form f() a b c and identifing a, b, and c f() ( 3)( 5) g() (7 )(9 ) k() 3( 11)( 1) h() ( 5)(3 1) d() ( 3) Identif whether each function is quadratic. Use a graph to check our answers. f() h() b() ( 1) k() 1 g() 16 3 m() 3 ( 9) State whether the parabola opens up or down and whether the -coordinate of the verte is the minimum value or the maimum value of the function. f() h() (5 )( 3) g() 7 q() ( )( 7) Graph each function and give the approimate coordinates of the verte. 16. k() h() p() ( )( 0.5) Algebra Workbook 7

29 5. Introduction to Solving Quadratic Equations Solve each equation. Give both eact solutions and approimate solutions to the nearest hundredth ( 3) ( ) ( 1) 161 Find the unknown length in each right triangle. Round answers to the nearest tenth. 11. A 1. L C Find the missing side length in right triangle ABC. Round answers to the nearest tenth. 1. a 15 and b a. and c b and c a 9.1 and b 7 8 c B J j K P 6.1 A r c b Q 3.5 R C a B 8 Workbook Algebra

30 5.3 Factoring Quadratic Epressions Factor each epression ( 7) 3( 7) ( 1) 3( 1) Factor each quadratic epression Solve each equation b factoring and appling the Zero-Product Propert Use factoring and the Zero-Product Propert to find the zeros of each quadratic function f() 1 6. g() h() b() k() q() Algebra Workbook 9

31 5. Completing the Square Complete the square for each quadratic epression in order to form a perfect-square trinomial. Then write the new epression as a binomial squared Solve b completing the square. Round our answers to the nearest tenth, if necessar Write each quadratic function in verte form. Find the coordinates of the verte and the equation of the ais of smmetr. 16. f() f() f() f() f() f() Workbook Algebra

32 5.5 The Quadratic Formula Use the quadratic formula to solve each equation. Round our answer to the nearest tenth ( )( 5) For each quadratic function, find the equation for the ais of smmetr and the coordinates of the verte. Round our answers to the nearest tenth, if necessar Algebra Workbook 31

33 5.6 Quadratic Equations and Comple Numbers Find the discriminant, and determine the number of real solutions. Then solve Perform the indicated addition or subtraction. ( 6 1i) ( i) (3 i) ( 9i) (11 i) ( 8i) ( 8 i) (7 i) ( 8 i) (7 i) (1 16i) (1 11i) ( 7 i) (3 3i) Write the conjugate of each comple number i Simplif. ( 1i) 7i 7 i 1 19i 5 i 19. i( 7 i) (3 i)(9 3i). 5 i ( 7 13i) (1 6i) 1 i 3 i 5 i 3i 3. ( 5i). (6 3i)( i) i 3 i 3 Workbook Algebra

34 5.7 Curve Fitting with Quadratic Models Solve a sstem of equations in order to find a quadratic function that fits each set of data points eactl. 1. (, 0), (0, ), (3, 5). (1, 6), (, 13), (, 1) 3. (, 9), (6, 1), (, 3). (0, 3), ( 1, 0), (1, ) 5. (, 9), (, 17), (1, ) 6. (3, 0), ( 1, 1), (, 3) 7. (0, ), (, 38), (, 0) 8. ( 3, 1), (, 5), ( 1, 7) ( 1, 1 ) 9. (, ), (6, 5), (8, 9) 10., (, 1), (3, 16) 11. (, 1), (3, ), ( 1, 3 1 ) (, 11), ( 1, 3), (, 77) A baseball plaer throws a ball. The table shows the height,, of the ball seconds after it is thrown. 13. Find a quadratic function to model the data. 1. What was the maimum height reached b the ball? 15. How long did it take the ball to reach its maimum height? 16. Use our model to predict the height of the ball 1.5 seconds after it was thrown. Time (seconds) Height (feet) Use our model to determine how man seconds it took for the ball to hit the ground. Algebra Workbook 33

35 5.8 Solving Quadratic Inequalities Solve each inequalit. Graph the solution on a number line. Round irrational numbers to the nearest hundredth Graph each inequalit and shade the solution region. 1 ( 3) ( 1) ( 3) Workbook Algebra

36 6.1 Eponential Growth and Deca Find the multiplier for each rate of eponential growth or deca. 1. 1% growth. 1% deca 3. 7% deca. 1% growth 5. 10% growth 6. 3% deca 7. 5.% deca % growth 9. 0.% growth % deca Evaluate each epression to the nearest thousandth for the given value of. 11. for ( ) for 3 ( 1 ) for 1. 7(0.5) for for for ( 1 ) 1 for ( 1 ) for () 3 for () for 6.5 Predict the result in each situation. 1. The population of a cit in 1990 was 1,15,11. The population was growing at a rate of about 5% per decade. Predict the population of the cit a. in the ear 000. b. in the ear The initial population of bacteria in a lab test is 00. The number of bacteria doubles ever 30 minutes. Predict the bacteria population at the end of a. two hours. b. three hours. Algebra Workbook 35

37 6. Eponential Functions Identif each function as linear, quadratic or eponential. 1. f() ( 1). g() 5 3. k() 11. g() w() h() b() ( ) ( ) 8. f() 9. h() 50(0.3) ( 3 ) 3 Tell whether each function represents eponential growth or deca. 10. f() 5.9(.6) 11. b() 13(0.7) 1. k() (0.15) 13. m() 51(.3) 1. w() z() 7(0.55) 16. h().5(0.8) 17. g() 0.8(3.) 18. a() 150(1.1) Find the final amount for each investment. 19. $1300 earning 5% interest compounded annuall for 10 ears 0. $850 earning % interest compounded annuall for 6 ears 1. $70 earning 6.% interest compounded semiannuall for 5 ears. $1100 earning 5.5% interest compounded semiannuall for ears 3. $300 earning.5% interest compounded quarterl for 3 ears. $1000 earning 6.5% interest compounded quarterl for ears 5. $5000 earning 6.3% interest compounded dail for 1 ear 6. $000 earning 5.5% interest compounded dail for 3 ears 36 Workbook Algebra

38 6.3 Logarithmic Functions Write each equation in logarithmic form ( 3 ) 3 6 ( 3 7 ) Write each equation in eponential form. 7. log 1 8. log 15, log log log 1. 1,61 log Solve each equation for. Round our answers to the nearest hundredth Find the value of v in each equation. 19. v log v log v log log 3. log. 3 log v 5. log 1 6. log 7. log 1 v 100 v 79 6 v 56 5 v 7 v Algebra Workbook 37

39 6. Properties of Logarithmic Functions Write each epression as a sum or a difference of logarithms. Then simplif, if possible. 1. log. log 7 10 ( 100) log7 (5 3 ). log3 15q 5. log 6 6. log 3a Write each epression as a single logarithm. Then simplif, if possible. 7. log 3 5 log log 5 log 5 9. log 8 log log 9 5 log 9 log log 1 6 log 1 1. log 3 81 log log b m log b log b 1. 3 log b (log b log b ) log b z log b log b z Evaluate each epression log log log log.7 0. log 3 log log 9 15 log Solve for and check our answers.. log (10) log (3 1) 3. log 3 log 3. log 5 ( 3) log 5 ( 1) 5. log 7 ( 1) log log 8 ( 3) log 8 ( 6) 7. log ( ) log (3 16) 8. log b 8 log b log b ( ) 9. log b ( 1) log b ( 11) 38 Workbook Algebra

40 6.5 Applications of Common Logarithms Solve each equation. Round our answers to the nearest hundredth ( 1 ) Evaluate each logarithmic epression to the nearest hundredth. 16. log log log log log log 9.. log log 8.5. log log log log log 0 9. log log Algebra Workbook 39

41 6.6 The Natural Base, e Evaluate each epression to the nearest thousandth. 1. e 8. e.5 3. e 5.. e 5. ln ln ln( 1.) 8. ln 1 9. ln 11 Write an equivalent eponential or logarithmic equation. 10. e ln e ln e ln e e ln Solve each equation for b using the natural logarithm function. Round our answers to the nearest hundredth $1000 is deposited in an account with an interest rate of 6.5%. Interest is compounded continuousl, and no deposits or withdrawals are made. Find the amount in the account at the end of three ears. 0 Workbook Algebra

42 6.7 Solving Equations and Modeling Solve each equation for. Write the eact solution and the approimate solution to the nearest hundredth, when appropriate log 1. log log e ln( 7) ln log 3 ( 1) ln ln 16 ln 1. ln ln( ) ln log log ln (1 e E In Eercises 17 and 18, use the equation M 3 log On Januar 17, 199, an earthquake with a magnitude of 6.6 injured more than 8000 people and caused an estimated $13 0 billion of damage to the San Fernando Valle in California. Find the amount of energ released b the earthquake. 18. On Januar 17, 1995, an earthquake struck Osaka, Koto, and Kobe, Japan, injuring more than 36,000 people and causing an estimated $100 billion of damage. The quake released about ergs of energ. Find the earthquake s magnitude on the Richter scale. Round our answer to the nearest tenth ) Algebra Workbook 1

43 7.1 An Introduction to Polnomials Determine whether each epression is a polnomial. If so, classif the polnomial b degree and b number of terms Evaluate each polnomial epression for the indicated value of. 3 3, , , , , , Write each sum or difference as a polnomial in standard form. (3 1 3 ) (5 3 7 ) ( ) ( 5 6 1) (8.8 3 ) ( ) Sketch the graph of each function. Describe the general shape of the graph. a() O k() 3 6 O 6 ( ) (9 3 18) f() O Workbook Algebra

44 7. Polnomial Functions and Their Graphs Graph each function and approimate an local maima or minima to the nearest tenth. P() P() 6 3 P() P() 3 Graph each function. Find an local maima or minima to the nearest tenth. Find the intervals over which the function is increasing and decreasing. 5. P() 3 3, P() 0.3 3, 7. P() 3 1., P().5 3 1, Describe the end behavior of each function Factor sales of passenger cars, in thousands, in the United States are shown in the table below. Find a quartic regression model for the data b using 0 for (Source: Bureau of the Census) Algebra Workbook 3

45 7.3 Products and Factors of Polnomials Write each product as a polnomial in standard form. 0.5( ) ( 10)( 3) ( )(5 3 7) ( )( 8)( 1) ( 5)( 1) (3 1) 3 Use substitution to determine whether the given linear epression is a factor of the given polnomial. 1; ; ; ; ; ; Divide b using long division. ( 7 30) ( 6) (6 5) (3 5) ( ) ( 1) Divide b using snthetic division. ( 3 1) ( 7) ( 3 3) ( 1) (5 3 3) ( 1) ( ) ( 8) ( 5 3 3) ( 3) For each function below, use snthetic division and substitution to find the indicated value. 1. P() 3 1; P(). P() 3 ; P(3) 3. P() 3 3 6; P(). P() 3 3 1; P( ) Workbook Algebra

46 7. Solving Polnomial Equations Use factoring to solve each equation Use graphing, snthetic division, and factoring to find all of the roots of each equation Use variable substitution and factoring to find all of the roots of each equation. If necessar, leave our answers in radical form Use a graph and the Location Principle to find the real zeros of each function. Give approimate values to the nearest tenth, if necessar. P() P() P() P() P() P() Algebra Workbook 5

47 7.5 Zeros of Polnomial Functions Find all the rational roots of each polnomial equation. P() P() P() P() P() P() Find all the zeros of each polnomial function. P() P() P() P() P() P() Find all real values of for which the functions are equal. Round our answers to the nearest hundredth. 13. P() 5, Q() 1 1. P() 3 5 3, Q() P() 3 1, Q() P() 3 1, Q() 1 Write a polnomial function, P, in standard form b using the given information. 17. The zeros of P() are 3,, and, and P(0) P(0) 96, and two of the three zeros are 3 and i. 6 Workbook Algebra

48 8.1 Inverse, Joint, and Combined Variation For Eercises 1, varies inversel as. Write the appropriate inverse-variation equation, and find for the given values of when 7; 5, 10, 16, and when ; 0.1, 5, 8, and when 5; 6, 15, 0, and when 0.; 0.5, 6, 10, and 16 For Eercises 5 8, varies jointl as and z. Write the appropriate joint-variation equation, and find for the given values of and z when and z 0.5; when.5 and z ; and z and z 7. 1 when and z 5; when and z 3 6 and z and z 5 For Eercises 9 1, z varies jointl as and and inversel as w. Write the appropriate combined-variation equation, and find z for the given values of,, and w. 9. z 30 when, 10, and w.5; 10. z 3. when 0., 8, and w ; 5, 6, and w 8 3, 6, and w z 3.75 when 6, 1, and w 8; 1. z.8 when 0., 10, and w 5; 0.05, 0, and w , 5, and w The apothem of a regular polgon is the perpendicular distance from the center of the polgon to a side. The area, A,ofa regular polgon varies jointl as the apothem, a, and the perimeter, p.a regular triangle with an apothem of 3 inches and a perimeter of 31. inches has an area of 6.8 square inches. Find the constant of variation and write a joint-variation equation. Then find the area of a regular triangle with an apothem of.3 inches and a perimeter of 1 inches. Algebra Workbook 7

49 8. Rational Functions and Their Graphs Determine whether each function below is a rational function. If so, find the domain. If the function is not rational, state wh not f() h() 3. 3 w() 1 Identif all vertical and horizontal asmptotes of the graph of each rational function. 1. k() 9 5. p() 3 ( 1.5) m() 7 Find the domain of each rational function. Identif all asmptotes and holes in the graph of each rational function h() 6 8. g() n() Sketch the graph of each rational function. Identif all asmptotes and holes in the graph of the function. 10. a() f() 1. b() Workbook Algebra

50 8.3 Multipling and Dividing Rational Epressions Simplif each rational epression Algebra Workbook 9

51 8. Adding and Subtracting Rational Epressions Simplif Write each epression as a single rational epression in simplest form Workbook Algebra

52 8.5 Solving Rational Equations and Inequalities Solve each equation. Check our solution Solve each inequalit. Check our solution Use a graphics calculator to solve each rational inequalit. Round answers to the nearest tenth Algebra Workbook 51

53 8.6 Radical Epressions and Radical Functions Find the domain of each radical function. f() 1 30 f() 7( ) f() 36 f() 5 f() f() 3 Find the inverse of each quadratic function. Then graph the function and its inverse in the same coordinate plane Evaluate each epression. Give eact answers , The volume of a sphere with diameter d is given b the equation V 1 6 πd3.solve this equation for d in terms of V. Then use our equation to find the diameter, to the nearest foot, of a sphere with a volume of 1000 cubic feet. 5 Workbook Algebra

54 8.7 Simplifing Radical Epressions Simplif each radical epression b using the Properties of nth Roots z 1 (80 5 ) 1 ( 16 3 ) 3 Simplif each product or quotient. Assume that the value of each variable is positive z z Find each sum, difference, or product. Give our answer in simplest radical form. (16 3 ) (9 ) (5 7 3) ( 3 1) ( 3 )(3 6 ) ( 7 5)(3 5) Write each epression with a rational denominator and in simplest form ( ) (6 8) 8 ( ) Algebra Workbook 53

55 8.8 Solving Radical Equations and Inequalities Solve each radical equation b using algebra. If the equation has no solution, write no solution. Check our solution Solve each radical inequalit b using algebra. If the inequalit has no solution, write no solution. Check our solution Solve each radical equation or inequalit b using a graph. Round solutions to the nearest tenth. Check our solution b an method Workbook Algebra

56 9.1 Introduction to Conic Sections Solve each equation for, graph the resulting equation, and identif the conic section Find the distance between P and Q, and find the coordinates of M, the midpoint of PQ. Give eact answers and approimate answers to the nearest hundredth when appropriate.. P(0, 0) and Q(5, 1) 5. P(, 1) and Q(1, 5) 6. P(1, ) and Q( 8, ) 7. P(7.5, 3) and Q( 1.5, 5) 8. P( 8, 8) and Q(, ) 9. P( 1, 1) and Q(1, ) Find the center, circumference, and area of the circle whose diameter has the given endpoints. 10. P(6, 0) and Q(1, 8) 11. P(0, 0) and Q(9, 0) 1. P(, 16) and Q(, 1) 13. P(3, 7) and Q(, 5) 1. P(10, 5) and Q(0, 6) 15. P( 8, 8) and Q(13, 3) Algebra Workbook 55

57 9. Parabolas Write the standard equation for each parabola graphed below F 6 O 6 8 V O F 6 directri 5 = O V(3, 1) directri Graph each equation. Label the verte, focus, and directri. 1 1 ( 1) ( ) Write the standard equation for the parabola with the given characteristics. 7. verte: (0, 0); focus: (0, 6) 8. verte: (10, 0); directri: 8 9. focus: (3, 0); directri: verte: (5, ); directri: verte: (6, 7); focus: (, 7) 1. focus: (9, 5); directri: 5 56 Workbook Algebra

58 9.3 Circles Write the standard equation for each circle graphed below O 6 O O Write the standard equation of a circle with the given radius and center. r 3 ; C(0, 0) r.5; C(, 1) r ; C( 3, 3) Graph each equation. Label the center and the radius. 56 ( 5) Write the standard equation for each circle. Then state the coordinates of its center, and give its radius. ( 3) ( 3) Algebra Workbook 57

59 9. Ellipses Write the standard equation for each ellipse O 8 6 O C ( 3, ) C (3, ) O Sketch the graph of each ellipse. Label the center, foci, vertices, and co-vertices. ( 1) ( ) ( 3) Write the standard equation for the ellipse with the given characteristics. 7. vertices: ( 5, 0) and (5, 0); co-vertices: (0, 15) and (0, 15) 8. foci: ( 10, 0) and (10, 0); co-vertices: (0, 3), (0, 3) 9. co-vertices: ( 0, 0) and (0, 0); foci: (0, 8) and (0, 8) 10. An ellipse is defined b Write the standard equation, and identif the coordinates of the center, vertices, co-vertices, and foci. 58 Workbook Algebra

60 9.5 Hperbolas Write the standard equation for each hperbola Graph each hperbola. Label the center, vertices, co-vertices, foci, and asmptotes. ( 1) ( 1) C (0, 0) For Eercises 5 7, write the standard equation for the hperbola with the given characteristics. 5. vertices: ( 10, 0) and ( 10, 0) ; co-vertices: (0, 15 ) and (0, 15 ) 6. foci: ( 5, ) and (5, ); vertices: ( 3, 0) and (3, 0) 7. center: (1, 1); vertices: (1, ) and (1, 6); co-vertices: (13, 1) and ( 11, 1) 8. A hperbola is defined b Write the standard equation, and identif the coordinates of the center, vertices, co-vertices, and foci. Algebra Workbook 59

61 9.6 Solving Nonlinear Sstems Use the substitution method to solve each sstem. If there are no real solutions, write none Use the elimination method to solve each sstem. If there are no real solutions, write none Solve each sstem b graphing. If there are no real solutions, write none Classif the conic section defined b each equation. Write the standard equation of the conic section, and sketch the graph Workbook Algebra

62 10.1 Introduction to Probabilit Find the probabilit of each event. 1. A blue card is drawn at random from a bag containing white cards, 1 red card, and 7 blue cards.. Frederique, who arrives home at 6: P.M., is home to receive a call that can come at an time between 6:0 and 6: A letter chosen at random from the letters of the word permutation is a vowel.. A card chosen at random from a standard 5-card deck is a heart or a diamond. 5. A card chosen at random from a standard deck is not an 8 or an ace. 6. A number cube is rolled, and a number greater than 3 and less than 6 results. 7. A letter chosen at random from the alphabet is not one of the 5 standard vowels. 8. A point on a 1-inch ruler is chosen at random and is located within an inch of an end of the ruler. A spinner is divided into three colored regions. You spin the spinner a total of 150 times. The results are recorded in the table. Find the eperimental probabilit of each event. 9. green 10. ellow 11. pink 1. not pink 13. not ellow Find the number of possible license plate numbers (with no letters or digits ecluded) for each of the following conditions: 1. 6 digits 15. letters followed b 3 digits 16. letters followed b 3 digits digits followed b letters 18. digits followed b letters followed b digits green ellow 65 pink 3 Algebra Workbook 61

63 10. Permutations Find the number of permutations of the first 7 letters of the alphabet for each situation. 1. taking all 7 letters at a time. taking 5 letters at a time 3. taking letters at a time. taking 3 letters at a time In how man was can 1 books be displaed on a shelf if the given number of books are available? 5. 1 books 6. 1 books books 8. 0 books Find the number of permutations of the letters in each word. 9. geometr 10. algebra 11. addition 1. calculus 13. mathematics 1. arithmetic 15. Lizette decorates windows for a department store. She plans to design a bab s room with a row of stuffed elephants and monkes along one wall. If she has 8 identical elephants and 10 identical monkes, in how man different was can the stuffed animals be displaed? 16. The 6 candidates for a student government office are invited to speak at an election forum. In how man different orders can the speak? 17. Representatives from 8 schools are represented at a school newspaper workshop. In how man different was can the 8 representatives be seated around a circular table? 18. Ten colleges are participating in a college fair. Booths will be positioned along one wall of a high school gmnasium. In how man different orders can the booths be arranged? 6 Workbook Algebra

64 10.3 Combinations Find the number of was in which each committee can be selected. 1. a committee of 5 people from a group of 8 people. a committee of people from a group of 16 people 3. a committee of people from a group of 7 people. a committee of 8 people from a group of 15 people 5. a committee of 3 people from a group of 9 people At a luncheon, guests are offered a selection of different grilled vegetables and 5 different relishes. In how man was can the following items be chosen? 6. vegetables and 3 relishes 7. 3 vegetables and relishes 8. vegetables and relishes 9. 3 vegetables and 3 relishes A bag contains 8 white marbles and 7 blue marbles. Find the probabilit of selecting each combination. 10. white and 3 blue white and blue 1. white and 1 blue Determine whether each situation involves a permutation or a combination. 13. A high school offers 5 foreign language programs. In how man was can a student choose programs? 1. In how man was can 0 members be chosen from a 60-member chorus to sing the national anthem at a graduation ceremon? 15. In how man was can a captain, co-captain, and team manager be chosen from among the 18 members of a volleball team? 16. First- through fourth-place prizes are to be awarded in an essa contest. In how man was can the winners be selected from among 15 entries? Algebra Workbook 63

65 10. Using Addition with Probabilit A card is drawn at random from a standard 5-card deck. Tell whether events A and B are inclusive or mutuall eclusive. Then find P(A or B). 1. A: The card is a heart.. A: The card is a number less than 5. B: The card is an 8. B: The card is a jack, a king, or a queen. 3. A: The card is black.. A: The card is not a diamond. B: The card is a number greater than. B: The card is a spade. 5. A: The card is red. 6. A: The card is a or a 3. B: The card is the ace of spades. B: The card is not a heart. A spinner is divided into 8 congruent regions numbered 1 through 8. The spinner is spun once. Find the probabilit of each event. 7. The number is even or divisible b The number is odd or greater than The number is less than or greater than The number is odd or divisible b. Two number cubes are rolled, and the numbers on the top faces are added. The table at right shows the possible outcomes. Find each probabilit. 11. The sum is odd or greater than The sum is less than 6 or greater than The sum is even or less than The sum is less than 8 or a multiple of The sum is less than or a multiple of 5. 6 Workbook Algebra

66 10.5 Independent Events Events D, E, F and G are independent, and P(D) 0., P(E) 0.1, P(F) 0., and P(G) 0.5. Find the probabilit of each combination of events. 1. P(D and E). P(D and F) 3. P(E and F). P(D and G) 5. P(D and E and F) 6. P(E and F and G) A bag contains 3 white marbles, red marbles, and 7 blue marbles. A marble is picked at random and is replaced. Then a second marble is picked at random. Find each probabilit. 7. Both marbles are blue. 8. The first marble is white and the second marble is red. 9. The first marble is white and the second marble is not white. 10. Neither marble is red. 11. The first marble is blue and the second marble is red. A number cube is rolled twice. On each roll, the number on the top face is recorded. Find the probabilit of each event. 1. The first number is greater than 5 and the second is less than Both numbers are greater than. 1. The first number is even and the second number is odd. 15. Both numbers are less than. 16. Neither number is greater than. A number cube is rolled, and two coins are tossed. Find the probabilit of each event. 17. The number on the cube is and both coins are heads. 18. The number on the cube is even, one coin shows heads, and one shows tails. 19. The number on the cube is greater than and both coins are tails. 0. The number on the cube is greater than and the coins show different sides. Algebra Workbook 65

67 10.6 Dependent Events and Conditional Probabilit Two number cubes are rolled, and the first cube shows 6. Find the probabilit of each event below. 1. The sum is 9.. Both numbers are even. 3. The sum is greater than 8.. The sum is greater than 9 and less than 1. A spinner that is divided into 8 congruent regions, numbered 1 through 8, is spun once. Let A be the event even and let B be the event 6. Find each of the following probabilities. 5. P(A) 6. P(B) 7. P(A and B) 8. P(A orb) 9. P(A B) 10. P(B A) A spinner that is divided into 5 congruent regions, numbered 1 through 5, is spun once. Let A be the event odd and let B be the event less than 3. Find each of the following probabilities. 11. P(A) 1. P(B) 13. P(A and B) 1. P(A orb) 15. P(A B) 16. P(B A) Let A and B represent events. 17. Given P(A and B) 0.5 and P(A) 0., find P(B A). 18. Given P(A and B) 3 and P(A) 5 3,find P(B A). 19. Given P(B A) and P(A) 5 5 8,find P(A and B). 0. Given P(B A) 0. and P(A) 0.16, find P(A and B). 1. Given P(B A) 0.5 and P(A and B) 0., find P(A).. Given P(B A) 0.8 and P(A and B) 0.5, find P(A). 66 Workbook Algebra

68 10.7 Eperimental Probabilit and Simulation Use a simulation with 10 trials to find an estimate for each probabilit. 1. In tosses of a coin, heads. In 5 tosses of a coin, tails 3. In rolls of a number cube, appears eactl 3 times. appears more than times. 3 appears twice. Trial Result Trial Result Trial Result estimate: estimate: estimate: Of 100 motorists observed at an intersection, 6 turned left, 7 went straight, and 7 turned right. Use a simulation with 10 trials to find an estimate for each probabilit.. Eactl of ever 5. At least 3 of ever 6. Fewer than of ever motorists turn right. motorists go straight. motorists turn left. Trial Result Trial Result Trial Result estimate: estimate: estimate: Algebra Workbook 67

69 11.1 Sequences and Series Write the first si terms of each sequence. b n.5n 1.. f n 1 n 1 t n n a 1 0; a n 3a n 1 10 a 1 1; a n a n a 1 5; a n 3a n 1 For each sequence below, write a recursive formula, and find the net three terms. 7. 1, 11, 11, 1331, , 78, 75, 7,... 9., 6, 18, 5, , 1,, 16, , 11, 38, 119,... 1., 1, 7, 37,... Write the terms of each series. Then evaluate n 1. n 1 Evaluate. 5 ( j 8j ) j m (n 1) 17. m 1 n 1 5 ( j 3) j (k 0.5) (a 3a 5) 0. k 1 a 1 n 1 (3.5n 5n.) 68 Workbook Algebra

70 11. Arithmetic Sequences Based on the terms given, state whether or not each sequence is arithmetic. If so, identif the common difference, d ,18, 1,,...., 5, 10, 17, , 9.7, 1., 1.7,...., 6, 9, 13.5, , 1 3, , 1 5, 5 8, 5.7, 3., 1.1,... Write an eplicit formula for the nth term of each arithmetic sequence , 7,, 11, , 7, 1, 9, , 16, 19,, , 13, 1, 11, , 0, 31,, , 7.3, 6,.7,... List the first four terms of each arithmetic sequence. t 1 50; t n t n t 1 7.5; t n t n t 1 0; t n t n 1 8 t n 0n 15 t n 0.5n t n 1n 3 Find the indicated arithmetic means arithmetic means between 1 and arithmetic means between 0 and arithmetic means between 50 and arithmetic means between 7 and arithmetic means between 0 and 16. arithmetic means between 8 and Algebra Workbook 69

71 11.3 Arithmetic Series Use the formula for an arithmetic series to find each sum Find each sum. 7. the sum of the first 5 natural numbers 8. the sum of the first 15 multiples of 3 9. the sum of the first 5 multiples of 10. the sum of the multiples of 5 from 75 to 315, inclusive 11. the sum of the multiples of 7 from 8 to 371, inclusive For each arithmetic series, find S ( ) ( ) ( 1) ( 18) ( 15) ( ) ( 1) Evaluate (n 7) ( 3j 3) 0. n 1 j ( 7 m). 15 (13 5b) 3. m 1 b 1 i 1 10 (10k ) k 1 ( 8i 1) 70 Workbook Algebra

72 11. Geometric Sequences Determine whether each sequence is geometric. If so, identif the common ratio, r, and give the net three terms. 1. 9, 5, 9, 81, , 80, 3, 1.8, , 0,, 1 5,.... 1, 18, 7, 0.5, , 36,, 16, ,, 3,,... List the indicated terms of each geometric sequence. 7. t 1 18; t n t n 1 ; 8. t 1 ; t n.5t n 1 ; 9. t 1 0; t n 0.5t n 1 ; first terms first 5 terms first terms t 0; t.5; t 5 t 16; t 6 6; t t ; t ; t 7 Write an eplicit formula for the nth term of each geometric sequence , 100, 0, 16, , 6, 1., 0., , 3, 5.6, 0.8, , 5, 1.5, 31.5, , 5, 1 1, , , 9, 5, 3, Find geometric means between 0. Find geometric means between 7 and and Find 3 geometric means between. Find 3 geometric means between 1 and and Find 3 geometric means between. Find geometric means between 1 and and 97. Algebra Workbook 71

73 11.5 Geometric Series and Mathematical Induction Find each sum. Round answers to the nearest tenth, if necessar. 1. S 0 for the geometric series S 15 for the geometric series S 6 for the series related to the geometric sequence 7, 1, 8, 56, For Eercises 6 9, refer to the geometric sequence 3, 6, 1,, Find t Find t Find S Find S 0. Evaluate. Round answers to the nearest hundredth, if necessar ( k 1 ) 10.8 n 1 1 5(0.5 k ) k 1 n 1 j 1 m 1 3 (3m ) 1. 6 (3) p ( 1) t k 17. p 1 t 1 k 1 Use mathematical induction to prove that the statement is true for ever natural number, n n 3 n (n 1) () k k 1 7 Workbook Algebra

74 11.6 Infinite Geometric Series Find the sum of each infinite geometric series, if it eists Find the sum of each infinite geometric series, if it eists. 0.8 n ( 11 9 ) m n 1 m 1 11 ( 1 9) k 1 k j t j 1 t k (0.0) b k 1 b 1 0(0.1) n 1 n 1 Write each decimal as a fraction in simplest form Write an infinite geometric series that converges to the given number Algebra Workbook 73