Sample Questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Sample Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the equation is linear or nonlinear. 1) - = A) linear nonlinear Objective: (1.1) Recognizing Linear Equations ) = 0.9 A) linear nonlinear Objective: (1.1) Recognizing Linear Equations 1) ) Solve the equation. 3) ( - 1) = ( + 1)( - 3) 3) A) - 3 {} C) Objective: (1.1) Solving Equations That Lead to Linear Equations ) = 8-1 A) {3} {} C) {-3} { 1} Objective: (1.1) Solving Equations That Lead to Linear Equations ) = A) {3.} {} C) {-7} {3.} Objective: (1.1) Solving Linear Equations Involving Decimals ) ) ) -3 + A) + 1 = C) ) Objective: (1.1) Solving Linear Equations Involving Fractions 7) -3-3 = - + A) {} {7} C) {-7} {-} Objective: (1.1) Solving Linear Equations with Integer Coefficients 8) 1 = A) {1} {0} C) {-1} {-1} Objective: (1.1) Solving Linear Equations with Integer Coefficients 7) 8) Write the sentence as an equation. Let the variable represent the number. 9) The sum of twice a number and is 9. A) = 9 + = 9 C) + = 9 - = 9 Objective: (1.) Converting Verbal Statements into Mathematical Statements 9) 1

2 Solve the problem. ) Kevin invested part of his $,000 bonus in a certificate of deposit that paid % annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that ear was $900, how much did Kevin invest in the mutual fund? A) $000 $000 C) $7000 $000 Objective: (1.) Solving Applications Involving Decimal Equations (Mone, Miture, Interest) 11) A bank loaned out $9,000, part of it at the rate of 1% per ear and the rest at a rate of 8% per ear. If the interest received was $780, how much was loaned at 1%? A) $8,000 $9,000 C) $0,000 $1,000 Objective: (1.) Solving Applications Involving Decimal Equations (Mone, Miture, Interest) 1) Center Cit East Parking Garage has a capacit of 3 cars more than Center Cit West Parking Garage. If the combined capacit for the two garages is 119 cars, find the capacit for each garage. A) Center Cit East: 7 cars Center Cit East: 73 cars Center Cit West: 73 cars Center Cit West: 83 cars C) Center Cit East: 73 cars Center Cit East: 83 cars Center Cit West: 7 cars Center Cit West: 73 cars Objective: (1.) Solving Applications Involving Unknown Numeric Quantities 13) Two friends decide to meet in Chicago to attend a Cubʹs baseball game. Rob travels 1 miles in the same time that Carl travels 10 miles. Robʹs trip uses more interstate highwas and he can average 3 mph more than Carl. What is Robʹs average speed? A) 3 mph mph C) 0 mph 71 mph Objective: (1.) Solving Applied Problems Involving Distance, Rate, and Time 1) An eperienced bank auditor can check a bankʹs deposits twice as fast as a new auditor. Working together it takes the auditors hours to do the job. How long would it take the eperienced auditor working alone? A) 8 hr hr C) 1 hr hr Objective: (1.) Solving Applied Working Together Problems ) 11) 1) 13) 1) Decide what number must be added to the binomial to make a perfect square trinomial. 1) + 1 A) 98 C) 9 7 Objective: (1.) Solving Quadratic Equations b Completing the Square 1) Solve the equation b completing the square. 1) = 0 A) C) 1-9, , , , 7 7 1) Objective: (1.) Solving Quadratic Equations b Completing the Square

3 Solve the equation b factoring. 17) 3-8 = 0 8 A) 3, , 0 C) 8, 0 {0} 3 17) Objective: (1.) Solving Quadratic Equations b Factoring and the Zero Product Propert Find the real solutions, if an, of the equation. Use the quadratic formula. 18) + + = 0 A) C) 1-7, , , no real solution 18) Objective: (1.) Solving Quadratic Equations Using the Quadratic Formula 19) = 0 A) , , ) C) -7-9, , Objective: (1.) Solving Quadratic Equations Using the Quadratic Formula Solve the equation using the square root propert. 0) ( + ) = 9 A) {1, } {0, 1} C) {-7, 7} {-, 1} Objective: (1.) Solving Quadratic Equations Using the Square Root Propert 0) Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. 1) - + = 0 1) A) two nonreal solutions two real solutions C) eactl one real solution Objective: (1.) Using the Discriminant to Determine the Tpe of Solutions of a Quadratic Equation Solve the problem. ) Janet is training for a triathlon. Yesterda she jogged for 1 miles and then ccled another 31. miles. Her speed while ccling was miles per hour faster than while jogging. If the total time for jogging and ccling was 3.7 hours, at what rate did she ccle? A) 1 miles per hour 1 miles per hour C) 1 miles per hour 13 miles per hour Objective: (1.) Solving Applications Involving Distance, Rate, and Time 3) The square of the difference between a number and 9 is 9. Find the number(s). A) 1, 1 C) 90 78, 8 Objective: (1.) Solving Applications Involving Unknown Numeric Quantities ) 3) 3

4 ) The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is square feet, find its dimensions. A) ft b ft ft b 8 ft C) 7 ft b ft ft b 9 ft Objective: (1.) Solving Geometric Applications ) George and Matt have a painting business. George has less eperience and it takes him 3 hours more to paint a medium sized room than it takes Matt. Working together the can paint a medium sized room in hours. How long does it take each of them working individuall? Round to the nearest tenth of an hour. A) George: 1.9 hours, Matt: 9.9 hours George: 1.0 hours, Matt: 9.0 hours C) George: 13.7 hours, Matt:.7 hours George: 1. hours, Matt: 11. hours Objective: (1.) Solving Working Together Applications ) A ball is thrown verticall upward from the top of a building 1 feet tall with an initial velocit of 18 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s = t - 1t. After how man seconds will the ball pass the top of the building on its wa down? A) 7 sec 1 sec C) sec 8 sec Objective: (1.) Using the Projectile Motion Model ) ) ) Solve the equation after making an appropriate substitution. 7) 1/ - 9 1/ + 18 = 0 A) {9, 3} {3, } C) {81, 19} {-3, -} Objective: (1.) Solving Equations That Are Quadratic in Form (Disguised Quadratics) 7) 8) /3-7 1/3 + = 0 A) {-1, -8} {8, 1} C) {-, -} {, } Objective: (1.) Solving Equations That Are Quadratic in Form (Disguised Quadratics) 8) Find all solutions. 9) = 0 A) {1, -, } {-, } C) {} {-1, 1, -} Objective: (1.) Solving Higher-Order Polnomial Equations 9) Solve the inequalit. Epress our answer using interval notation. 30) k A) - 1, 17 17, C) -, , - 1, 17 30) Objective: (1.8) Solving an Absolute Value ʺGreater Thanʺ Inequalit 31) - < 1 A) (-, -8) (-, 0) C) (-8, 0) (-0, 8) Objective: (1.8) Solving an Absolute Value ʺLess Thanʺ Inequalit 31)

5 Solve the equation. 3) = 7 A) {-1, -13, 0, 1} {-1, -13, 1} C) {-13, -1, 0, 1} {-1, 1, -1, 1} Objective: (1.8) Solving an Absolute Value Equation 3) Solve the polnomial inequalit. Epress the solution in interval notation. 33) ( + )( - ) 0 A) (-, -] [, ) (-, -) (, ) C) [-, ] (-, ) Objective: (1.9) Solving Polnomial Inequalities 3) ( - 1)( + 8) > 0 A) (-8, 1) (-, -1) (8, ) C) (-, -8) (1, ) (-8, ) Objective: (1.9) Solving Polnomial Inequalities 33) 3) Solve the rational inequalit. Epress the solution in interval notation. 3) < 1 A) (-, -1) (-1, 8) C) (-, -1) (8, ) (-1, ) 3) Objective: (1.9) Solving Rational Inequalities 3 + < A) (-, -) (0, ) (-, -) (-, 0) C) (-, ) (, ) (-, -) (0, ) Objective: (1.9) Solving Rational Inequalities 3) 3) Determine whether the points A, B, and C form a right triangle. 37) A = (-, 7); B = (-, 11); C = (-, ) A) Yes No Objective: (.1) Finding the Distance between Two Points Using the Distance Formula 37) Find the distance d(a, between the points A and B. 38) A = (1, ); B = (-3, -) A) 8 C) 33 3 Objective: (.1) Finding the Distance between Two Points Using the Distance Formula 38) Find the midpoint of the line segment joining the points A and B. 39) A = (3, ); B = (9, 3) A) (-, ), C) (1, 8), Objective: (.1) Finding the Midpoint of a Line Segment Using the Midpoint Formula 39) Sketch the graph for the equation b plotting points.

6 0) = + 3 0) A) C) Objective: (.1) Graphing Equations b Plotting Points Determine whether the indicated ordered pair lies on the graph of the given equation. 1) =, (3, -3) A) Yes No Objective: (.1) Graphing Equations b Plotting Points 1) Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which ais it lies.

7 ) (-1, -) ) - - A) Quadrant III Quadrant III C) Quadrant IV Quadrant II Objective: (.1) Plotting Ordered Pairs Classif the function as a polnomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. t - 3) h(t) = t 3 3) - 9t A) rational function; (-, 0) (0, ) rational function; (-, ) C) rational function; (-, -3) (-3, 0) (0, 3) (3, ) rational function; (-, ) (, ) Objective: (3.1) Determining the Domain of a Function Given the Equation 7

8 ) h() = + 8 A) rational function; (-, 0) (0, ) rational function; (-, ) C) rational function; (-8, ) rational function; (-, -8) (-8, ) Objective: (3.1) Determining the Domain of a Function Given the Equation ) Determine whether the equation defines as a function of. ) = A) function not a function Objective: (3.1) Determining Whether Equations Represent Functions ) ) = A) function not a function Objective: (3.1) Determining Whether Equations Represent Functions ) Determine whether the relation represents a function. If it is a function, state the domain and range. 7) 7) Alice Brad Carl snake cat dog A) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} function domain: {Alice, Brad, Carl} range: {snake, cat, dog} C) not a function Objective: (3.1) Understanding the Definitions of Relations and Functions Evaluate the function at the indicated value. 8) Find f(1) when f() = ) A) 3-3 C) Objective: (3.1) Using Function Notation; Evaluating Functions 9) Find f(1) when f() = A) - 0 C) Objective: (3.1) Using Function Notation; Evaluating Functions 9) 8

9 The graph of a function f is given. Use the graph to answer the question. 0) What is the -intercept? 0) - - A) (0, ) (0, 17.) C) (0, -1) (0, -0) Objective: (3.) Determining Information about a Function from a Graph 1) Is f(3) positive or negative? 1) - - A) positive negative Objective: (3.) Determining Information about a Function from a Graph 9

10 ) Find the values of, if an, at which f has a relative maimum. What are the relative maima? 3 1 ) A) f has a relative maimum at = 0; the relative maimum is 1 f has no relative maimum C) f has a relative maimum at = 3; the relative maimum is 1 f has a relative maimum at = -3 and 3; the relative maimum is 0 Objective: (3.) Determining Relative Maimum and Relative Minimum Values of a Function Use the graph to determine the functionʹs domain and range. Write the domain and range in interval notation. 3) 3) A) domain: (-, -1) or (-1, ) range: (-, -1) or (-1, ) C) domain: [-1, ) range: [-1, ) domain: (-, ) range: (-, ) domain: (-, ) range: [-1, ) Objective: (3.) Determining the Domain and Range of a Function from Its Graph Find the -intercept(s) and the -intercept of the function. ) h() = A) (1, 0), (-, 0), (0, ) (1, 0), (, 0), (0, ) C) (-1, 0), (-, 0), (0, ) (-1, 0), (, 0), (0, ) Objective: (3.) Determining the Intercepts of a Function )

11 Determine algebraicall whether the function is even, odd, or neither. ) f() = 3 A) even odd C) neither Objective: (3.) Determining Whether a Function Is Even, Odd, or Neither ) ) f() = A) even odd C) neither Objective: (3.) Determining Whether a Function Is Even, Odd, or Neither ) 7) f() = A) even odd C) neither Objective: (3.) Determining Whether a Function Is Even, Odd, or Neither 7) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 8) (-1, 0) 8) A) increasing constant C) decreasing Objective: (3.) Determining Whether a Function Is Increasing, Decreasing, or Constant 9) (- 1, 0) 9) - - A) increasing constant C) decreasing Objective: (3.) Determining Whether a Function Is Increasing, Decreasing, or Constant 11

12 Based on the graph, determine the range of f. if - < - 0) f() = if - < 8 3 if 8 1 0) (8, 8) (-, ) (-, ) (1,.3) (-, ) (8, ) A) [0, ) [0, 3 1] C) [0, 8) [0, 8] Objective: (3.3) Analzing Piecewise-Defined Functions Find the rule that defines each piecewise-defined function. 1) 1) (0, ) (3, ) (-3, 0) - - A) f() = - if f() 3 if 0 3 = + 3 if if 0 < 3 C) f() = + if if 0 < 3 f() = 3 + if if 0 < 3 Objective: (3.3) Analzing Piecewise-Defined Functions Graph the function. 1

13 ) f() = ) - - A) C) Objective: (3.3) Sketching the Graphs of the Basic Functions 13

14 3) f() = 3) - - A) C) Objective: (3.3) Sketching the Graphs of the Basic Functions 1

15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. ) A cellular phone plan had the following schedule of charges: ) Basic service, including 0 minutes of calls nd 0 minutes of calls Additional minutes of calls $0.00 per month $0.07 per minute $0. per minute What is the charge for 00 minutes of calls in one month? What is the charge for 0 minutes of calls in one month? Construct a function that relates the monthl charge C for minutes of calls. Objective: (3.3) Solving Applications of Piecewise-Defined Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. ) f() = -( + 1) + ) A)

16 C) Objective: (3.) Using Combinations of Transformations to Graph Functions ) f() = ) A)

17 C) Objective: (3.) Using Horizontal Shifts to Graph Functions 7) f() = ) A)

18 C) Objective: (3.) Using Horizontal Shifts to Graph Functions 8) f() = 8) - - A)

19 C) Objective: (3.) Using Horizontal Stretches and Compressions to Graph Functions 9) f() = - 9) - - A)

20 C) Objective: (3.) Using Reflections to Graph Functions 70) f() = ) - - A)

21 C) Objective: (3.) Using Reflections to Graph Functions 71) f() = ) A)

22 C) Objective: (3.) Using Vertical Shifts to Graph Functions 7) f() = 1 7) - - A)

23 C) Objective: (3.) Using Vertical Stretches and Compressions to Graph Functions 73) f() = ) - - A)

24 C) Objective: (3.) Using Vertical Stretches and Compressions to Graph Functions Find the domain of the composite function f g. Write the domain in interval notation. 7) f() = 8 +, g() = + A) (-, ) (-, -13) (-13, ) C) (-, -7) (-7, -) (-, ) (-, 13) (13, ) Objective: (3.) Determining the Domain of Composite Functions 7) Evaluate. 7) Find (f - g)(-) when f() = + 1 and g() = +. A) 7 19 C) Objective: (3.) Evaluating a Combined Function 7) For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. 7) f() = 7-8; g() = - 7; Find f - g. 7) A) (f - g)() = 9-1; (-, 1) (1, ) (f - g)() = - 1; (-, ) C) (f - g)() = - 1; (-, 3) (3, ) (f - g)() = - + 1; (-, ) Objective: (3.) Finding Combined Functions and Their Domains 77) f() = 3 - ; g() = -8 + ; Find f + g. A) (f + g)() = - + ; (-, ) (f + g)() = + ; (-,, ) 77) C) (f + g)() = -; (-, ) (f + g)() = ; (-, 3 8 ) ( 3 8, ) Objective: (3.) Finding Combined Functions and Their Domains Find the intersection of the given intervals. 78) (-, 0) [-, ] A) [-, 0) (-, ] C) (-, -] (0, ] Objective: (3.) Finding the Intersection of Intervals 78) For the given functions f and g, find the requested composite function value. 79) f() = + 3, g() = 3; Find (f g)(). A) 3 1 C) Objective: (3.) Forming and Evaluating Composite Functions 79)

25 80) f() = +, g() = + 3; Find (g g)(1). A) 7 C) 3 Objective: (3.) Forming and Evaluating Composite Functions 80) Use the graph to evaluate the epression. 81) Find (f f)(-1) and (g g)() f() g() 81) A) (f f)(-1) = 1; (g g)() = (f f)(-1) = ; (g g)() = 0 C) (f f)(-1) = 3; (g g)() = (f f)(-1) = 7; (g g)() = 0 Objective: (3.) Forming and Evaluating Composite Functions Use the horizontal line test to determine whether the function is one -to-one. 8) 8) A) Yes No Objective: (3.) Determining Whether a Function Is One-to-One Using the Horizontal Line Test The function f is one-to-one. Find its inverse. 83) f() = - 3, 0 A) f -1 () = C) f -1 () = f -1 () = f -1 () = ) Objective: (3.) Finding the Inverse of a One-to-One Function

26 8) f() = A) f -1 () = C) f -1 () = f -1 () = f -1 () = ) Objective: (3.) Finding the Inverse of a One-to-One Function 8) f() = 3 + A) f -1 () = 3 - f -1 () = - C) f -1 () = 3 + f -1 1 () = 3-8) Objective: (3.) Finding the Inverse of a One-to-One Function The function f is one-to-one. State the domain and the range of f and f -1. Write the domain and range in set-builder notation. 8) f() = 3-8) A) f(): D = 3, R is all real numbers; f -1 (): D is all real numbers, R = 3 f(): D = 3, R = 0 ; f -1 (): D = 0, R = 3 C) f(): D = 3, R = 0 ; f -1 (): D is all real numbers, R = 3 f(): D = 0, R = 0 ; f -1 (): D = 0, R = 3 Objective: (3.) Finding the Inverse of a One-to-One Function Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same aes. 87) f() = 87)

27 A) C) Objective: (3.) Sketching the Graphs of Inverse Functions Decide whether or not the functions are inverses of each other. + 88) f() =, g() = + A) Yes No Objective: (3.) Understanding and Verifing Inverse Functions 88) 89) f() = + 3, -3; g() = + 3 A) Yes No Objective: (3.) Understanding and Verifing Inverse Functions 89) Determine whether the function is one-to-one. 90) h() = ) A) One-to-one Not one-to-one Objective: (3.) Understanding the Definition of a One-to-One Function 91) f() = - 3 A) One-to-one Not one-to-one Objective: (3.) Understanding the Definition of a One-to-One Function 91) 7

28 Analze the graph and write the equation of the function it represents in standard form f() = a( - h) + k. 9) 9) verte: (-, -) -intercept: 0, A) = 1 ( + ) + = -( + ) - C) = ( + ) + = - 1 ( + ) - Objective: (.1) Determining the Equation of a Quadratic Function Given Its Graph 93) 93) 8 0 verte: (-3, 0) (0, 9) A) f() = ( + 3) f() = -( + 3) C) f() = -( - 3) f() = ( - 3) Objective: (.1) Determining the Equation of a Quadratic Function Given Its Graph First rewrite the quadratic function in standard form b completing the square, then find an -intercepts and an -intercepts. 9) f() = ) A) No -intercepts; -intercept: -7 -intercepts: 8 and 9; -intercept: -7 C) -intercepts: 8 and -9; -intercept: 17 -intercepts: -8 and -9; -intercept: 7 Objective: (.1) Graphing Quadratic Functions b Completing the Square Find the range of the quadratic function in interval notation. 9) f() = A) (-, -] (-, -] C) [, ) [-, ) Objective: (.1) Graphing Quadratic Functions b Completing the Square 9) 8

29 Rewrite the quadratic function in standard form b completing the square. 9) f() = A) f() = ( - ) - 8 f() = ( + ) + 8 C) f() = ( - ) + 8 f() = ( + ) - 8 Objective: (.1) Graphing Quadratic Functions b Completing the Square 9) Find the coordinates of the verte of the quadratic function. 97) f() = A) (-3, 18) (-, 3) C) (3, -3) (3, -18) Objective: (.1) Graphing Quadratic Functions b Completing the Square 97) 98) f() = A) (, -1) (1, -1) C) (-, -17) (-1, -) Objective: (.1) Graphing Quadratic Functions b Completing the Square 98) Graph the quadratic function using its verte, ais of smmetr, and intercepts. 99) f() = ) A) verte (-1, ) intercept 0, 17 verte (-1, ) intercept (0, 8)

30 C) verte (1, ) intercept 0, 17 verte (1, ) intercept (0, 8) Objective: (.1) Graphing Quadratic Functions Using the Verte Formula Use the quadratic function to determine if the function has a maimum or minimum value and then find this maimum or minimum value. 0) f() = A) minimum at - 39, - 1 C) minimum at - 1, - 39 maimum at - 39, - 1 maimum at - 1, - 39 Objective: (.1) Graphing Quadratic Functions Using the Verte Formula 0) 1) f() = A) maimum at (9, 3) minimum at (0, 3) C) minimum at (9, 0) maimum at (-3, -9) Objective: (.1) Graphing Quadratic Functions Using the Verte Formula 1) Graph the quadratic function using its verte, ais of smmetr, and intercepts. ) f() = - 0 )

31 A) verte (3, 9) intercept (0, 18) verte (-3, 9) intercept (0, 18) C) verte (-3, -9) intercepts (0, 0), (-, 0) verte (3, -9) intercepts (0, 0), (, 0) Objective: (.1) Graphing Quadratic Functions Using the Verte Formula Find the range of the quadratic function in interval notation. 3) f() = -7( - 3) - A) (-, 3] [-, ) C) (-, -] [-3, ) Objective: (.1) Graphing Quadratic Functions Written in Standard Form 3) Find the ais of smmetr of the quadratic function. ) f() = -7( - ) - A) = -7 = - C) = - = Objective: (.1) Graphing Quadratic Functions Written in Standard Form ) Sketch the graph of the quadratic function. 31

32 ) f() = ( + ) + ) A) C) Objective: (.1) Graphing Quadratic Functions Written in Standard Form Find the ais of smmetr of the quadratic function. ) f() = ( + ) + 7 A) = -7 = C) = - = 7 Objective: (.1) Graphing Quadratic Functions Written in Standard Form ) 3

33 Without graphing, determine whether the graph of the quadratic function opens up or opens down. 7) f() = A) opens down opens up Objective: (.1) Understanding the Definition of a Quadratic Function and Its Graph 7) Solve the problem. 8) A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has 3 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 3,3 ft 30,97 ft C) 1,88 ft 77 ft Objective: (.) Maimizing Area Functions 9) The manufacturer of a CD plaer has found that the revenue R (in dollars) is R(p) = -p + 190p, when the unit price is p dollars. If the manufacturer sets the price p to maimize revenue, what is the maimum revenue to the nearest whole dollar? A) $1,0 $,8 C) $1,011,0 $0,0 Objective: (.) Maimizing Functions in Economics 1) A projectile is fired from a cliff 00 feet above the water at an inclination of to the horizontal, with a muzzle velocit of 10 feet per second. The height h of the projectile above the water is given b h() = , where is the horizontal distance of the projectile from the base (10) of the cliff. How far from the base of the cliff is the height of the projectile a maimum? A) 71. ft ft C) 11. ft 937. ft Objective: (.) Maimizing Projectile Motion Functions 111) Which of the following polnomial functions might have the graph shown in the illustration below? 8) 9) 1) 111) A) f() = ( - ) ( - 1) f() = ( - ) ( - 1) C) f() = ( - )( - 1) f() = ( - )( - 1) Objective: (.3) Determining a Possible Equation of a Polnomial Function Given Its Graph 33

34 Use the end behavior of the graph of the polnomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative. 11) 11) A) even; positive odd; positive C) odd; negative even; negative Objective: (.3) Determining the End Behavior of Polnomial Functions Find the - and -intercepts of f. 113) f() = ( - )( - 1) A) -intercepts: 0,, 1; -intercept: -intercepts: 0,, 1; -intercept: 0 C) -intercepts: 0, -, -1; -intercept: -intercepts: 0, -, -1; -intercept: 0 Objective: (.3) Determining the Intercepts of a Polnomial Function 113) Determine the real zeros of the polnomial and their multiplicities. Then decide whether the graph touches or crosses the -ais at each zero. 11) f() = 3( + )( - ) 11) A), multiplicit, crosses -ais, multiplicit, touches -ais C) -, multiplicit 1, crosses -ais;, multiplicit, touches -ais -, multiplicit 1, touches -ais;, multiplicit, crosses -ais Objective: (.3) Determining the Real Zeros of Polnomial Functions and Their Multiplicities 3

35 Graph the polnomial function. 11) f() = - ( + 1)( + 3) ) A) C) Objective: (.3) Sketching the Graph of a Polnomial Function 11) f() = - 11)

36 A) C) Objective: (.3) Sketching the Graph of a Polnomial Function Use the graph of a power function and transformations to sketch the graph of the polnomial function. 117) f() = ) - - 3

37 A) C) Objective: (.3) Sketching the Graphs of Power Functions 118) f() = 3 - ( + ) 118)

38 A) C) Objective: (.3) Sketching the Graphs of Power Functions 119) f() = 1 ( - ) )

39 A) C) Objective: (.3) Sketching the Graphs of Power Functions State whether the function is a polnomial function or not. If it is, give its degree. 10) f() = A) Yes; degree 8 Yes; degree C) Not a polnomial Yes; degree 7 Objective: (.3) Understanding the Definition of a Polnomial Function 10) Find the domain of the rational function. 11) f() = A) all real numbers { 3, -} C) { -3, } { 3, -3, -} Objective: (.) Finding the Domain and Intercepts of Rational Functions 11) Give the equation of the horizontal asmptote, if an, of the function. 1) f() = A) = 0 = C) = none Objective: (.) Identifing Horizontal Asmptotes 1) 39

40 Give the equation of the slant asmptote, if an, of the function. 13) f() = A) none = + 1 C) = + 1 = - Objective: (.) Identifing Slant Asmptotes 13) Find the vertical asmptotes, if an, of the graph of the rational function. 1) f() = + 9 A) = 0 and = -9 no vertical asmptote C) = -9 = 0 and = 9 Objective: (.) Identifing Vertical Asmptotes 1) Graph the function. - 1) f() = ) A)

41 C) Objective: (.) Sketching Rational Functions 1) f() = 3 ( + 1)( + 3) 1) A)

42 C) Objective: (.) Sketching Rational Functions For the following rational function, identif the coordinates of all removable discontinuities and sketch the graph. Identif all intercepts and find the equations of all asmptotes. 17) f() = ( - 9)( + ) ( 17) - )( + 3) A) removable discontinuities: -,, -3, 3 ; -intercept: (3, 0), -intercept: 0, 3 ; asmptotes: =, =

43 removable discontinuit at (-3, 0); -intercept: (-3, 0), -intercept: 0, 3 ; asmptotes: = -, = C) removable discontinuities: -, 1, (-3, 0); -intercept: (-3, 0), -intercept: 0, - 3 ; asmptotes: =, = removable discontinuit at -3, - 3 ; -intercept: (3, 0), -intercept: 0, - 3 ; asmptotes: = -, = Objective: (.) Sketching Rational Functions Having Removable Discontinuities Graph the function using transformations. 3

44 - 18) f() = ) - - A) C) Objective: (.) Using Transformations to Sketch the Graphs of Rational Functions Use transformations to graph the function.

45 19) f() = ( - 3) - 19) A) C) Objective: (.1) Sketching the Graphs of Eponential Functions Using Transformations

46 130) f() = e + 130) A) C) Objective: (.1) Sketching the Graphs of Eponential Functions Using Transformations Solve the problem. 131) An original investment of $7000 earns 7% interest compounded continuousl. What will the investment be worth in 3 ears? Round to the nearest cent. A) $87.30 $ C) $873.7 $83.7 Objective: (.1) Solving Applications of Eponential Functions 13) Suppose that $000 is invested at an interest rate of.% per ear, compounded continuousl. What is the balance after ears?round to the nearest cent. A) $31.00 $77.0 C) $.00 $7.0 Objective: (.1) Solving Applications of Eponential Functions 131) 13)

47 133) A rumor is spread at an elementar school with 100 students according to the model N = 100(1 - e -0.1d ) where N is the number of students who have heard the rumor and d is the number of das that have elapsed since the rumor began. How man students will have heard the rumor after das? A) 1 students 89 students C) 0 students 3 students Objective: (.1) Solving Applications of Eponential Functions 133) Solve the equation. 13) 3-3 = ) A) 1 9 {3} C) {-3} {9} Objective: (.1) Solving Eponential Equations b Relating the Bases 13) 3 ( - ) = 81 A) {3} {-3} C) {} {} 13) Objective: (.1) Solving Eponential Equations b Relating the Bases Evaluate the logarithm without the use of a calculator. 13) log ) A) C) 1 1 Objective: (.) Evaluating Logarithmic Epressions Find the domain of the function. 137) f() = ln(- - ) A) (-, -) (-, ) C) (-, ) (, ) 137) Objective: (.) Finding the Domain of Logarithmic Functions Graph the function. 138) f() = log )

48 A) C) Objective: (.) Sketching the Graphs of Logarithmic Functions Using Transformations 139) f() = log 139) - - 8

49 A) C) Objective: (.) Sketching the Graphs of Logarithmic Functions Using Transformations Evaluate the epression without the use of a calculator, and then verif our answer using a calculator. 10) e ln 8 A) e 8 7 C) 8 ln 8 Objective: (.) Understanding the Characteristics of Logarithmic Functions 10) Write the eponential equation as an equation involving a logarithm. 11) 7 3 = 33 A) log 3 = 33 log 33 = 3 C) log 7 = 3 log 33 = ) Objective: (.) Understanding the Definition of a Logarithmic Function Write the logarithmic equation as an eponential equation. 1) log = 3 A) = 3 3 = C) 3 = 3 = Objective: (.) Understanding the Definition of a Logarithmic Function 1) Use the properties of logarithms to evaluate the epression without the use of a calculator. 13) log A) 1 C) Objective: (.) Understanding the Properties of Logarithms 13) 9

50 Write the eponential equation as an equation involving a common logarithm or a natural logarithm. 1) = 0 A) log 0 = log = 0 C) log 0 = log = 0 1) Objective: (.) Using the Common and Natural Logarithms Write the logarithmic equation as an eponential equation. 1) log(0) = A) 0 = 0 0 = C) = 0 1/ = 0 Objective: (.) Using the Common and Natural Logarithms 1) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 1) log 11 1) A) 1 log 11 1 log log C) log log log 11 + log Objective: (.3) Epanding and Condensing Logarithmic Epressions Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic epressions. 17) log 0 - log 17) A) log 00 log 8 C) log 0 1/ 3 Objective: (.3) Epanding and Condensing Logarithmic Epressions Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 18) log 3 b z 18) A) log b + 3log b - log b z log b + 3log b + log b z C) log b + log b 3 + log b z log b + log b 3 - log b z Objective: (.3) Epanding and Condensing Logarithmic Epressions Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic epressions. 19) ln( - 11) - 8 ln 19) A) ln ( - 11) 8 ln 0( - 11) C) ln 8 ( - 11) ln Objective: (.3) Epanding and Condensing Logarithmic Epressions ( - 11) 8 Solve the equation. ) log ( + ) - log ( - ) = log A) {-1} {1} C) ) Objective: (.3) Solving Logarithmic Equations Using the Logarithm Propert of Equalit 0

51 Solve the logarithmic equation. 11) log = log 7 A) = 9 = 7 C) = 7 = 1 Objective: (.3) Using the Change of Base Formula 11) Use the change of base formula and a calculator to evaluate the logarithm. Round our answer to two decimal places. 1) log.. 1) A) C) Objective: (.3) Using the Change of Base Formula Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 7 13) log 13) 13 A) log 7 + log 13 log 13 - log 7 C) log 7 log 13 log 7 - log 13 Objective: (.3) Using the Product Rule, Quotient Rule, and Power Rule for Logarithms 1) log 1 1) A) 8 - log C) - log - log Objective: (.3) Using the Product Rule, Quotient Rule, and Power Rule for Logarithms Solve the equation. 1) 3 t - 1 = 7 1 A) {3} C) ) Objective: (.) Solving Eponential Equations Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 1) e + = A) {-3.31} {-3.08} C) {1.79} {-.1} Objective: (.) Solving Eponential Equations 1) Solve the equation. 17) log ( - ) = 1 - log 3 3 A) {-} {-7} C) {} {7} Objective: (.) Solving Logarithmic Equations 18) log3 + log3( - ) = A) {3} {7} C) {-3, 7} Objective: (.) Solving Logarithmic Equations 17) 18) 1

52 Solve the problem. 19) The half-life of silicon-3 is 7 ears. If 0 grams is present now, how much will be present in 300 ears? (Round our answer to three decimal places.) A).77 0 C) Objective: (.) Eponential Growth and Deca 10) Kimberl invested $3000 in her savings account for 7 ears. When she withdrew it, she had $ Interest was compounded continuousl. What was the interest rate on the account? Round to the nearest tenth of a percent. A) 3.% 3.3% C) 3.% 3.% Objective: (.) Solving Compound Interest Applications 0,000 11) The logistic growth function f(t) = models the number of people who have become ill e-1.t with a particular infection t weeks after its initial outbreak in a particular communit. How man people were ill after weeks? A) 1, people 0,000 people C) 0,00 people 0 people Objective: (.) Solving Logistic Growth Applications 1) Sand manages a ceramics shop and uses a 0 F kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches 180 F before opening it and removing the ceramic pieces. If room temperature is 70 F and the gauge reads 0 F in minutes, how long must she wait before opening the kiln? Round our answer to the nearest whole minute. A) 0 min 313 min C) 88 min 9 min Objective: (.) Using Newtonʹs Law of Cooling 19) 10) 11) 1) Solve the sstem of linear equations using the elimination method. 13) z = z = z = 33 A) (8,, ) (1,, -8) C) (8,, ) (-8,, 1) Objective: (7.) Solving a Sstem of Linear Equations Using the Elimination Method 13) Solve the problem. 1) A deli sells three sizes of chicken sandwiches: the small chicken sandwich contains ounces of meat and sells for $3.00; the regular chicken sandwich contains 8 ounces of meat and sells for $3.0; and the large chicken sandwich contains ounces of meat and sells for $.00. A customer requests a selection of each size for a reception. She and the manager agree on a combination of sandwiches made from pounds ounces of chicken for a total cost of $178. How man of each size sandwich will be in this combination? (Note: 1 pound = 1 ounces) A) small sandwiches, medium sandwiches, 18 large sandwiches. 18 small sandwiches, 1 medium sandwiches, large sandwiches. C) small sandwiches, 1 medium sandwiches, 1 large sandwiches. 0 small sandwiches, medium sandwiches, large sandwiches. Objective: (7.) Solving Applied Problems Using a Sstem of Linear Equations Involving Three Variables 1)

53 Solve the sstem of linear equations. If the sstem has infinitel man solutions, describe the solution with an ordered triple in terms of variable z. 1) + + z = 7 1) - + z = 7 + 3z = 1 A) - 3z + 7, z, z 3z - + 7, z, z 3z C) - - 7, z, z 3z - - 7, z, z Objective: (7.) Solving Consistent, Dependent Sstems of Linear Equations in Three Variables 1) - + 3z = z = z = 0 A) (-8, -7, 9) no solution C) (, -7, -1) (8, -7, -) Objective: (7.) Solving Inconsistent Sstems of Linear Equations in Three Variables 1) Determine if the given ordered triple is a solution of the sstem. 17) (-, -1, ) + + z = z = z = - A) solution not a solution Objective: (7.) Verifing the Solution of a Sstem of Linear Equations in Three Variables 17) Determine whether the sstem corresponding to the given augmented matri is dependent or inconsistent. If it is dependent, give the solution ) ) A) dependent; (8, -) inconsistent C) dependent; (-8, ) dependent; (-8,, -9) Objective: (7.3) Determining Whether a Sstem Has No Solution or Infinitel Man Solutions Use Gaussian elimination to solve the linear sstem b finding an equivalent sstem in triangular form. 19) + + z = z = z = 7 A) (-1, -, ) no solution C) (, -, -1) (-1,, -) Objective: (7.3) Solving a Sstem of Linear Equations Using Gaussian Elimination 19) Solve the problem. 170) Ron attends a cocktail part (with his graphing calculator in his pocket). He wants to limit his food intake to 13 g protein, 1 g fat, and 17 g carbohdrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, g fat, and 9 g carbohdrate; the spic meatballs have 1 g protein, 7 g fat, and 1 g carbohdrate; and the deviled eggs have 13 g protein, 1 g fat, and g carbohdrate. How man of each snack can he eat to obtain his goal? A) mushrooms, 3 meatballs, 9 eggs mushrooms, meatballs, eggs C) 3 mushrooms, 9 meatballs, eggs 9 mushrooms, meatballs, 3 eggs Objective: (7.3) Solving Applied Problems Using a Sstem of Linear Equations Involving Three Variables 170) 3

54 Use Gauss-Jordan elimination to solve the linear sstem and determine whether the sstem has a unique solution, no solution, or infinitel man solutions. If the sstem has infinitel man solutions, describe the solution as an ordered triple involving variable z. 171) z = ) + 9z = z = - 1 A) C) 19z 19z + 0, - 9z + 3, z - 19z + 0, - 9z + 3, z 9z + 0, + 3, z 19z 9z + 0, - - 3, z Objective: (7.3) Solving Consistent, Dependent Sstems of Linear Equations in Three Variables 17) + + z = z = = 1 A) (0, -, 1) (1, -, 0) C) (-, 0, -1) no solution Objective: (7.3) Solving Inconsistent Sstems of Linear Equations in Three Variables 17) Use Gauss-Jordan elimination to solve the linear sstem and determine whether the sstem has a unique solution, no solution, or infinitel man solutions. If the sstem has infinitel man solutions, describe the solution as an ordered triple involving variable z. 173) + + z = 7 173) - + z = 7 A) (-3z + 1, z - 7, z) - 3 z + 7, 1 z, z C) (, 1, ) (8, -3, ) Objective: (7.3) Solving Linear Sstems Having Fewer Equations Than Variables Use Gaussian elimination and matrices to solve the sstem of linear equations. Write our final augmented matri in triangular form and then solve for each variable using back substitution. 17) - + z = 1 + z = + + z = 17) A) (0,, ) (, 0, ) C) (,, 0) (0,, ) Objective: (7.3) Using an Augmented Matri to Solve a Sstem of Linear Equations A sstem of nonlinear equations is given. Sketch the graph of the equation of the sstem and then determine the number of real solutions to the sstem. Do not solve the sstem.

55 17) = - 1 = ) A) Two One C) One Two Objective: (7.) Determining the Number of Solutions to a Sstem of Nonlinear Equations Determine the real solutions to the sstem of nonlinear equations. 17) + = = - A) (, -3), (-, 3) (1, 3), (-1, -3) C) (, 3), (, -3), (-, 3), (-, -3) (1, 3), (1, -3), (-1, 3), (-1, -3) Objective: (7.) Solving a Sstem of Nonlinear Equations Using Substitution, Elimination, or Graphing 17)

56 177) + = 0 ( - ) + = 0 A) (1, 7), (1, -7) (7, 1), (7, -1) C) (1, 7), (1, -7), (-1, 7), (-1, -7) (7, 1), (7, -1), (-7, 1), (-7, -1) Objective: (7.) Solving a Sstem of Nonlinear Equations Using Substitution, Elimination, or Graphing 177) 178) = = 0 A) (, 1), (-, -1) (, 1), (, -1), (-, 1), (-, -1) C) (-1, ), (1, -) (1, ), (-1, ), (1, -), (-1, -) Objective: (7.) Solving a Sstem of Nonlinear Equations Using Substitution, Elimination, or Graphing 178) 179) = + = A) (, 8), (-, 8) (, 8), (, -8) C) (, 8), (, -8), (-, 8), (-, -8) (8, ), (8, -) Objective: (7.) Solving a Sstem of Nonlinear Equations Using Substitution, Elimination, or Graphing 179) 180) + = + = A) (0, -), (-, 0) (,-), (-, -) C) (0, ), (, 0) (0, 0), (, -) Objective: (7.) Solving a Sstem of Nonlinear Equations Using the Substitution Method 181) + = + = A) (-, ), (1, 1) (, -), (1, 1) C) (, 0), (-1, 3) (0, ), (3, -1) Objective: (7.) Solving a Sstem of Nonlinear Equations Using the Substitution Method 18) = = - 1 A) 7, 7, - 1, -1-1, -1 C) 7, 1, -1, - 1 (-7, 7), (1, -1) 7 180) 181) 18) Objective: (7.) Solving a Sstem of Nonlinear Equations Using the Substitution Method 183) = 1 + = 8 A) (-, -8), (-8, -), (-, 8), (-8, ) (, 8), (8, ), (, -8), (8, -) C) (, -), (-, -8), (8, ), (-8, -) (, 8), (-, -8), (, -8), (-, 8) Objective: (7.) Solving a Sstem of Nonlinear Equations Using the Substitution Method 183) Solve the problem. 18) The diagonal of the floor of a rectangular office cubicle is feet longer than the length of the cubicle and feet longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessar. A) width: 9.7 feet, length:. feet width: 3.9 feet, length: 9.7 feet C) width: feet, length: 9 feet width: feet, length: 11 feet Objective: (7.) Solving Applied Problems Using a Sstem of Nonlinear Equations 18)

57 Let represent one number and let represent the other number. Use the given conditions to write a sstem of nonlinear equations. Solve the sstem and find the numbers. 18) The sum of the squares of two numbers is 13. The sum of the two numbers is. Find the two 18) numbers. A) -3 and - and 3 C) -3 and ; - and 3 and 3; -3 and - Objective: (7.) Solving Applied Problems Using a Sstem of Nonlinear Equations Determine if each ordered pair is a solution to the given sstem of inequalities in two variables. 18) 3 - = -17 = ) (i) (, 3); (ii) (-, 11) A) (i) No; (ii) Yes (i) No; (ii) No C) (i) Yes; (ii) Yes (i) Yes; (ii) No Objective: (7.) Determining If an Ordered Pair Is a Solution to a Sstem of Linear Inequalities in Two Variables 187) = + = ) (i) (, -9); (ii) (-9, -) A) (i) Yes; (ii) Yes (i) No; (ii) No C) (i) No; (ii) Yes (i) Yes; (ii) No Objective: (7.) Determining If an Ordered Pair Is a Solution to a Sstem of Linear Inequalities in Two Variables Determine if the ordered pair is a solution to the given inequalit. 188) 3-9; (-0.,.) A) Yes No Objective: (7.) Determining If an Ordered Pair Is a Solution to an Inequalit in Two Variables 188) Graph the inequalit. 189) + < 189)

58 A) C) Objective: (7.) Graphing a Linear Inequalit in Two Variables 190) ) - - 8

59 A) C) Objective: (7.) Graphing a Linear Inequalit in Two Variables 191) ) - - 9

60 A) C) Objective: (7.) Graphing a Linear Inequalit in Two Variables 19) )

61 A) C) Objective: (7.) Graphing a Nonlinear Inequalit in Two Variables Graph the sstem of inequalities. 193) )

62 A) C) Objective: (7.) Graphing a Sstem of Linear Inequalities in Two Variables 19) < > )

63 A) C) Objective: (7.) Graphing a Sstem of Linear Inequalities in Two Variables 19) )

64 A) C) Objective: (7.) Graphing a Sstem of Linear Inequalities in Two Variables 19) < > 19)

65 A) C) Objective: (7.) Graphing a Sstem of Linear Inequalities in Two Variables 197) ) - >

66 A) C) Objective: (7.) Graphing a Sstem of Nonlinear Inequalities in Two Variables 198) + 198)

67 A) no solution C) Objective: (7.) Graphing a Sstem of Nonlinear Inequalities in Two Variables 7