Precalculus Fall Final Review Chapters 1-6 and Chapter 7 sections 1-4 Name

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1 Precalculus Fall Final Review Chapters 1-6 and Chapter 7 sections 1- Name SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! Graph the equation using a graphing utilit. Use a graphing utilit to approimate the intercepts rounded to two decimal places, if necessar. Use the TABLE feature to help establish the viewing window. 1) 3 - = 6 Find the midpoint of the line segment joining the points P1 and P. ) P1 = (-0.6, -0.); P = (-., -1. ) Solve. 7) A vendor has learned that, b pricing hot dogs at $1., sales will reach 79 hot dogs per da. Raising the price to $.00 will cause the sales to fall to 6 hot dogs per da. Let be the number of hot dogs the vendor sells at dollars each. Write a linear equation that relates the number of hot dogs sold per da,, to the price. List the intercepts for the graph of the equation. ) = + 9 Find the center (h, k) and radius r of the circle with the given equation. 3) = 36 Decide whether or not the points are the vertices of a right triangle. ) (9, -6), (1, -), (1, -9) Find the slope of the line containing the two points. 9) (-9, 6); (-9, ) Graph the equation b plotting points. ) = Solve the equation algebraicall. Verif our solution with a graphing utilit. ) = Graph the equation. 6) + ( - ) = Find the distance d(p1, P) between the points P1 and P. 11) P1 = (7, -7); P = (3, -) Graph the equation using a graphing utilit. Use a graphing utilit to approimate the intercepts rounded to two decimal places, if necessar. 1) 3 - = 3 1

2 Find the center (h, k) and radius r of the circle. Graph the circle. 13) = 0 Find the slope of the line and sketch its graph. 17) 3 + = Write the standard form of the equation of the circle with radius r and center (h, k). 1) r = ; (h, k) = (0, -) Solve. 1) A school has just purchased new computer equipment for $17, The graph shows the depreciation of the equipment over ears. The point (0, 17,000 ) represents the purchase price and the point (, 0) represents when the equipment will be replaced. Write a linear equation in slope-intercept form that relates the value of the equipment,, to ears after purchase. Use the equation to predict the value of the equipment after ears Find the slope and -intercept of the line. 16) - 7 = 1 Solve. 1) When making a telephone call using a calling card, a call lasting 6 minutes cost $1.9. A call lasting 1 minutes cost $3.9. Let be the cost of making a call lasting minutes using a calling card. Write a linear equation that relates the cost of a making a call,, to the time. Plot the point in the -plane. Tell in which quadrant or on what ais the point lies. 19) (0, -1) - - Use a graphing utilit to approimate the real solutions, if an, of the equation rounded to two decimal places. 0) = 0 Write the equation of a function that has the given characteristics. 1) The graph of =, shifted 7 units downward

3 Use a graphing utilit to graph the function over the indicated interval and approimate an local maima and local minima. If necessar, round answers to two decimal places. ) f() = ; (-, ) Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 3) f() = 1 3 Answer the question about the given function. 7) Given the function f() = +, list the - -intercepts, if an, of the graph of f. The graph of a function is given. Decide whether it is even, odd, or neither. ) The graph of a function f is given. Use the graph to answer the question. ) Is f(3) positive or negative? 9) It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = 0.7t + 1, for t >. Find the approimate number of fish that can be caught if ou fish for 0 minutes. Locate an intercepts of the function. 30) f() = -3 + if < 1-3 if 1 - For the graph of the function = f(), find the absolute maimum and the absolute minimum, if it eists. 31) - Find the average rate of change for the function between the given values. ) f() = + ; from to Determine algebraicall whether the function is even, odd, or neither. 6) f() = 1 3

4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the function with the graph that best describes the situation. 3) The amount of rainfall as a function of time, if the rain fell more and more softl. A) D) SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! B) The graph of a function is given. Decide whether it is even, odd, or neither. 33) C) Find the value for the function. 3) Find f() when f() =

5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the correct function to the graph. 3) The graph of a function is given. Decide whether it is even, odd, or neither. 3) A) = - B) = + C) = 1 - D) = - SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! The graph of a function is given. Decide whether it is even, odd, or neither. 36) -π -π π π For the given functions f and g, find the requested function and state its domain. 37) f() = - ; g() = - 1 Find f g. The graph of a function f is given. Use the graph to answer the question. 39) For what numbers is f() = 0? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to the function listed whose graph most resembles the one given. 0) A) reciprocal function B) square root function C) absolute value function D) square function

6 SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! 1) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1. and then add 3 to the result. Epress F as a linear function of c. Graph the function using its verte, ais of smmetr, and intercepts. ) f() = ) A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has 30 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? Graph the function using its verte, ais of smmetr, and intercepts. 7) f() = Find the verte and ais of smmetr of the graph of the function. 3) f() = - + Determine the quadratic function whose graph is given. ) (0, 3) ) A rock falls from a tower that is 160 ft high. As it is falling, its height is given b the formula h = t. How man seconds will it take for the rock to hit the ground (h = 0)? (-, -1) ) The quadratic function f() = models the median, or average, age,, at which U.S. men were first married ears after In which ear was this average age at a minimum? (Round to the nearest ear.) What was the average age at first marriage for that ear? (Round to the nearest tenth.) 6

7 9) The following scatter diagram shows heights (in inches) of children and their ages. Height (inches) 1) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost Graph the function f b starting with the graph of = and using transformations (shifting, compressing, stretching, and/or reflection). ) f() = Age (ears) What happens to height as age increases? Graph the function. State whether it is increasing, decreasing, or constant.. 0) f() = Solve the inequalit. 3) < Graph the function using its verte, ais of smmetr, and intercepts. ) f() =

8 Plot a scatter diagram. ) Draw a scatter diagram of the given data. Find the equation of the line containing the points (.,.1) and (.6, 3.0 ). Graph the line on the scatter diagram Graph the function f b starting with the graph of = and using transformations (shifting, compressing, stretching, and/or reflection). 9) f() = Determine the average rate of change for the function. 60) p() = - + Use a graphing utilit to find the equation of the line of best fit. Round to two decimal places, if necessar. 6) Managers rate emploees according to job performance and attitude. The results for several randoml selected emploees are given below. Use the graph to find the vertical asmptotes, if an, of the function. 61) Performance Attitude ) A flare fired from the bottom of a gorge is visible onl when the flare is above the rim. If it is fired with an initial velocit of 176 ft/sec, and the gorge is 0 ft deep, during what interval can the flare be seen? (h = -16t + v 0 t + h 0.) Determine the average rate of change for the function. ) F() = - - List the potential rational zeros of the polnomial function. Do not find the zeros. 6) f() = Use the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 63) f() = - 1-6

9 Graph the function using transformations. 6) f() = Solve the inequalit algebraicall. Epress the solution in interval notation. 71) ( - 11)( + 1) ( - )( + ) 0 For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 7) f() = 1 3 ( - ) - State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 6) f() = ( -1) 66) For what positive numbers will the cube of a number eceed 9 times its square? Find the indicated intercept(s) of the graph of the function. 67) -intercept of f() = ( - 6) ( + 11) 3 Use the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 6) f() = Use the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 73) f() = Find the - and -intercepts of f. 7) f() = ( + 6)( - )( + ) Give the equation of the oblique asmptote, if an, of the function. 7) h() = Use the graph to find the vertical asmptotes, if an, of the function. 76) Find the indicated intercept(s) of the graph of the function. 69) -intercept of f() = Give the equation of the horizontal asmptote, if an, of the function. 70) g() = Find the intercepts of the function f(). 77) f() = - 3 Find the indicated intercept(s) of the graph of the function. 7) -intercept of f() =

10 State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 79) f() = Use the graph of the function f to solve the inequalit. 0) f() < 0 6) f() = log3( + 1) and g() = log3( - ). Solve g() = 19. What point is on the graph of g? Solve the equation. 7) 3 = 7 ) log3 + log3( - ) = Write as the sum and/or difference of logarithms. Epress powers as factors. 9) log Find the domain of the composite function f g. 1) f() = ; g() = ) During its first ear of operation, 00,000 people visited Rave Amusement Park. Si ears later, the number had grown to 3,000. If the number of visitors to the park obes the law of uninhibited growth, find the eponential growth function that models this data. 3) Between 7:00 AM and :00 AM, trains arrive at a subwa station at a rate of trains per hour (0.17 trains per minute). The following formula from statistics can be used to determine the probabilit that a train will arrive within t minutes of 7:00 AM. F(t) = 1 - e -0.17t Determine how man minutes are needed for the probabilit to reach 0%. Solve the equation. ) log 3 ( + ) = + log 3 ( - 3 ) 90) The long jump record, in feet, at a particular school can be modeled b f() = ln( + 1) where is the number of ears since records began to be kept at the school. What is the record for the long jump 1 ears after record started being kept? Round our answer to the nearest tenth. For the given functions f and g, find the requested composite function value. 91) f() = 7 +, g() = -1/; Find (g f)(3). Use transformations to graph the function. Determine the domain, range, and horizontal asmptote of the function. 9) f() = ) 1 7 = 9

11 93) The formula P = 1.7e -0.1 gives the average atmospheric pressure, P, in pounds per square inch, at an altitude, in miles above sea level. Find the average atmospheric pressure for an altitude of.3 miles. Round our answer to the nearest tenth. Epress as a single logarithm. 9) 7ln ( - ) - ln MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. 9) Decide whether the composite functions, f g and g f, are equal to. 99) f() =, g() = 0) A full cooked turke is taken out of an oven set at 00 C (Celsius) and placed in a sink of chilled water of temperature C. After 3 minutes, the temperature of the turke is measured to be 0 C. How long (to the nearest minute) will it take for the temperature of the turke to reach 1 C? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)e kt. (Round our answer to the nearest minute.) Find the period. 1) = - cos(! + ) - - A) = log - B) = - log C) = log( - ) D) = log( - ) SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! Epress as a single logarithm. 96) log + log ( - 169) - log 9 - log ( - 13) Solve the equation. 97) log11 = ) Before eercising, an athlete measures her air flow and obtains a = 0.6 sin! t where a is measured in liters per second and t is the time in seconds. If a > 0, the athlete is inhaling; if a < 0, the athlete is ehaling. The time to complete one complete inhalation/ehalation sequence is a respirator ccle. What is the amplitude? What is the period? What is the respirator ccle? Graph a over two periods beginning at t = 0. 1 a 9) Gillian has $,000 to invest in a mutual fund. The average annual rate of return for the past five ears was 1.%. Assuming this rate, determine how long it will take for her investment to double. -1 t 11

12 Convert the angle in degrees to radians. Epress the answer as multiple of!. 3) 7 Find an equation for the graph. ) Find the eact value. Do not use a calculator. 111) cot Use the properties of the trigonometric functions to find the eact value of the epression. Do not use a calculator. 11) sin + cos Find the amplitude. 113) = -3 cos +! In the problem, sin θ and cos θ are given. Find the eact value of the indicated trigonometric function. 11) sin θ = 3, cos θ = 3 Find tan θ. ) For what numbers θ is f(θ) = csc θ not defined? Find the phase shift. 6) = -3 sin 1 -! If A denotes the area of the sector of a circle of radius r formed b the central angle θ, find the missing quantit. If necessar, round the answer to two decimal places. 7) r =. centimeters, θ =! radians, A =? Use the even-odd properties to find the eact value of the epression. Do not use a calculator. ) sec -! 6 Convert the angle in radians to degrees. 9) - 7! 6 1) A rotating beacon is located ft from a wall. If the distance from the beacon to the point on the wall where the beacon is aimed is given b a = sec (!t), where t is in seconds, find a when t = 0.0 seconds. Round our answer to the nearest hundredth. Find (i) the amplitude, (ii) the period, and (iii) the phase shift. 11) = - 1 sin( + 3!) Write the equation of a sine function that has the given characteristics. 116) Amplitude: Period: 3! Phase Shift: -! 3 Find the area A. Round the answer to three decimal places. 117)! m Find the eact value of the epression if θ =. Do not use a calculator. 11) f(θ) = cos θ Find 11f(θ). Use the even-odd properties to find the eact value of the epression. Do not use a calculator. 119) sec (-60 ) 1

13 Find the eact value of the epression. Do not use a calculator. 10) sin! 3 - cos! 6 Solve the equation. Give a general formula for all the solutions. 13) cos(θ) = Use a calculator to find the value of the epression rounded to two decimal places. 11) sin -1 3 Solve the equation on the interval 0 θ <!. 133) cot θ -! = 1 Find the eact solution of the equation. 1) -sin -1 () =! Find the eact value, if an, of the composite function. If there is no value, sa it is "not defined". Do not use a calculator. 13) sin(sin -1 1.) Find the eact solution of the equation. 1) 3 sin -1 =! 1) -3 sin -1 () =! 13) 1 + cos θ = sin θ Use a calculator to solve the equation on the interval 0 θ <!. Round the answer to two decimal places. 13) csc θ = - Establish the identit. 136) 1 - cot v 1 + cot v + 1 = sin v 137) (tan v + 1) + (tan v - 1) = sec v 13) 1 + csc sec = cos + cot Find the eact value of the epression. 16) cos sin ) csc + csc - 1 cot = csc - 1 csc ) sin cos ) 1 - sin t cos t = cos t 1 + sin t 1) tan(cos -1 1) 19) sec ) sin cos -1 - Solve the equation on the interval 0 θ <!. 131) cos θ - 1 = 0 13

14 Answer Ke Testname: FALL FINAL REVIEW 017 1) (0, -1), (1.67, 0) ID: PCEGU Objective: (1.1) Use a Graphing Utilit to Approimate Intercepts ) (-1., -1) ID: PCEGU Objective: (1.1) Use the Midpoint Formula 3) (h, k) = (-9, -); r = 6 ID: PCEGU Objective: (1.) Work with the General Form of the Equation of a Circle ) No ID: PCEGU Objective: (1.1) Use the Distance Formula ) {, 6} ID: PCEGU Objective: (1.3) Solve Equations Using a Graphing Utilit 6) - - ) ID: PCEGU Objective: (1.) Know How to Graph Ke Equations 11) ID: PCEGU Objective: (1.1) Use the Distance Formula 1) (0, -6.), (-3.37, 0), (3.37, 0) ID: PCEGU Objective: (1.1) Use a Graphing Utilit to Approimate Intercepts 13) (h, k) = (-3, -6); r = ID: PCEGU Objective: (1.) Graph a Circle 7) = ID: PCEGU Objective: (1.) Find the Equation of a Line Given Two Points ) (0, -3), (-9, 0), (0, 3) ID: PCEGU Objective: (1.) Find Intercepts from an Equation 9) undefined ID: PCEGU Objective: (1.) Calculate and Interpret the Slope of a Line ID: PCEGU Objective: (1.) Work with the General Form of the Equation of a Circle 1) + ( + ) = ID: PCEGU Objective: (1.) Write the Standard Form of the Equation of a Circle 1) = ,000 ; value after ears is $,00.00; ID: PCEGU Objective: (1.) Find the Equation of a Line Given Two Points 1

15 Answer Ke Testname: FALL FINAL REVIEW ) slope = 7 ; -intercept = ID: PCEGU Objective: (1.) Identif the Slope and -Intercept of a Line from Its Equation 17) slope = - 3 ) local maimum at (0, 1) local minimum at (, -3) ID: PCEGU Objective: (.3) Use Graphing Utilit to Approimate Local Maima/Minima & Determine Where Func is Increasing/Decreasing 3) ID: PCEGU Objective: (1.) Graph Lines Written in General Form Using Intercepts 1) = ID: PCEGU Objective: (1.) Find the Equation of a Line Given Two Points 19) - - -ais ID: PCEGU Objective: (1.1) Graph Equations b Hand b Plotting Points 0) no solution ID: PCEGU Objective: (1.3) Solve Equations Using a Graphing Utilit 1) = - 7 ID: PCEGU Objective: (.) Graph s Using Vertical and Horizontal Shifts ID: PCEGU6..- Objective: (.) Graph s Using Compressions and Stretches ) negative ID: PCEGU6..-3 Objective: (.) Obtain Information from or about the Graph of a ) 1 ID: PCEGU Objective: (.3) Find the Average Rate of Change of a 6) even ID: PCEGU6.3.- Objective: (.3) Identif Even and Odd s from the Equation 7) none ID: PCEGU6..-3 Objective: (.) Obtain Information from or about the Graph of a ) even ID: PCEGU Objective: (.3) Determine Even and Odd s from a Graph 9) About 6 fish ID: PCEGU Objective: (.1) Find the Value of a 30) (0, ) ID: PCEGU6..- Objective: (.) Graph Piecewise-defined s 1

16 Answer Ke Testname: FALL FINAL REVIEW ) Absolute maimum: none; Absolute minimum: f(1) = ID: PCEGU Objective: (.3) Use a Graph to Locate the Absolute Maimum and the Absolute Minimum 3) A ID: PCEGU6..-6 Objective: (.) Obtain Information from or about the Graph of a 33) even ID: PCEGU Objective: (.3) Determine Even and Odd s from a Graph ) verte (, 1) intercept (0, 6) ) - 3 ID: PCEGU6.1.- Objective: (.1) Find the Value of a 3) A ID: PCEGU6..1- Objective: (.) Graph s Using Vertical and Horizontal Shifts 36) odd ID: PCEGU Objective: (.3) Determine Even and Odd s from a Graph 37) (f g)() = ( - )( - 1); { 1 } ID: PCEGU Objective: (.1) Form the Sum, Difference, Product, and Quotient of Two s 3) odd ID: PCEGU Objective: (.3) Determine Even and Odd s from a Graph 39) -60, 70, 0 ID: PCEGU6..- Objective: (.) Obtain Information from or about the Graph of a 0) A ID: PCEGU Objective: (.) Graph the s Listed in the Librar of s 1) F(c) = 1.c + 3 ID: PCEGU Objective: (3.1) Build Linear Models from Verbal Descriptions ID: PCEGU Objective: (3.3) Graph a Quadratic Using Its Verte, Ais, and Intercepts 3) (, ); = ID: PCEGU Objective: (3.3) Identif the Verte and Ais of Smmetr of a Quadratic ) 3. s ID: PCEGU Objective: (3.) Solve Inequalities Involving a Quadratic ) 19, 3.7 ears old ID: PCEGU Objective: (3.) Build Quadratic Models from Verbal Descriptions 6) 11, ft ID: PCEGU Objective: (3.3) Find the Maimum or Minimum Value of a Quadratic 7) verte (-6, -36) intercepts (0, 0), (- 1, 0) ID: PCEGU Objective: (3.3) Graph a Quadratic Using Its Verte, Ais, and Intercepts 16

17 Answer Ke Testname: FALL FINAL REVIEW 017 ) f() = ID: PCEGU Objective: (3.3) Find a Quadratic Given Its Verte and One Other Point 9) Height increases as age increases. ID: PCEGU Objective: (3.) Draw and Interpret Scatter Diagrams 0) increasing 6 ) verte (1, 9) intercepts (, 0), (-, 0), (0, ) ID: PCEGU Objective: (3.3) Graph a Quadratic Using Its Verte, Ais, and Intercepts ) = ID: PCEGU Objective: (3.1) Determine Whether a Linear Is Increasing, Decreasing, or Constant 1) 3 thousand automobiles ID: PCEGU Objective: (3.) Build Quadratic Models from Verbal Descriptions ) ID: PCEGU Objective: (3.3) Graph a Quadratic Using Transformations 3) -, 3 ID: PCEGU Objective: (3.) Draw and Interpret Scatter Diagrams 6) = ID: PCEGU Objective: (3.) Use a Graphing Utilit to Find the Line of Best Fit 7) < t < 6 ID: PCEGU Objective: (3.) Solve Inequalities Involving a Quadratic ) 0 ID: PCEGU Objective: (3.1) Use Average Rate of Change to Identif Linear s ID: PCEGU Objective: (3.) Solve Inequalities Involving a Quadratic 17

18 Answer Ke Testname: FALL FINAL REVIEW 017 9) ID: PCEGU Objective: (3.3) Graph a Quadratic Using Transformations 60) -1 ID: PCEGU Objective: (3.1) Use Average Rate of Change to Identif Linear s 61) = 3 ID: PCEGU6..-1 Objective: (.) Find the Vertical Asmptotes of a Rational 6) ± 1 6, ± 1 3, ± 1, ± 3, ± 1, ± ID: PCEGU6..- Objective: (.) Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polnomial 63) -, ; f() = ( - )( + )( + ) ID: PCEGU Objective: (.) Find the Real Zeros of a Polnomial 6) - - ID: PCEGU6..- Objective: (.) Demonstrate Additional Understanding and Skills 6) No; is raised to non-integer power ID: PCEGU Objective: (.1) Identif Polnomial s and Their Degree 66) { > 9}; (9, ) ID: PCEGU Objective: (.6) Solve Polnomial Inequalities Algebraicall and Graphicall 67) 0, ID: PCEGU Objective: (.) Analze the Graph of a Rational 6) 1, 1; f() = ( - 1) (3 + 1) ID: PCEGU Objective: (.) Find the Real Zeros of a Polnomial 69) 0, 7 1 ID: PCEGU Objective: (.) Analze the Graph of a Rational 70) no horizontal asmptotes ID: PCEGU6..3- Objective: (.) Find the Horizontal or Oblique Asmptotes of a Rational 71) (-, -) [-1, ) [11, ) ID: PCEGU Objective: (.6) Solve Rational Inequalities Algebraicall and Graphicall 7) 0, multiplicit, touches -ais;, multiplicit 1, crosses -ais; -, multiplicit 1, crosses -ais ID: PCEGU Objective: (.1) Identif the Real Zeros of a Polnomial and Their Multiplicit 73) 3 ; f() = (3 - )( + ) ID: PCEGU6..3- Objective: (.) Find the Real Zeros of a Polnomial 7) -intercepts: -6, -, ; -intercept: -96 ID: PCEGU Objective: (.1) Analze the Graph of a Polnomial 7) no oblique asmptote ID: PCEGU Objective: (.) Find the Horizontal or Oblique Asmptotes of a Rational 1

19 Answer Ke Testname: FALL FINAL REVIEW ) = 0 ID: PCEGU Objective: (.) Find the Vertical Asmptotes of a Rational 77) -intercepts: 0,, -; -intercept: 0 ID: PCEGU Objective: (.) Find the Real Zeros of a Polnomial 7) (0, 0) ID: PCEGU Objective: (.) Analze the Graph of a Rational 79) No; is raised to a negative power ID: PCEGU Objective: (.1) Identif Polnomial s and Their Degree 0) (-3, ) (, ) ID: PCEGU Objective: (.6) Solve Polnomial Inequalities Algebraicall and Graphicall 1) { -11} ID: PCEGU6.1.- Objective: (.1) Find the Domain of a Composite ) f(t) = 00,000e 0.3t ID: PCEGU Objective: (.) Find Equations of Populations That Obe the Law of Uninhibited Growth 3) 3.00 min ID: PCEGU6..-3 Objective: (.) Solve Logarithmic Equations ) 9 ID: PCEGU Objective: (.6) Solve Logarithmic Equations ) {-} ID: PCEGU6.3.- Objective: (.3) Solve Eponential Equations 6) {}, (, 19) ID: PCEGU Objective: (.6) Solve Logarithmic Equations 7) {-3} ID: PCEGU Objective: (.3) Solve Eponential Equations ) {7} ID: PCEGU Objective: (.6) Solve Logarithmic Equations 9) log( - 1) + log( + + 1) - 3 log ID: PCEGU Objective: (.) Write a Logarithmic Epression as a Sum or Difference of Logarithms 90).9 ft ID: PCEGU Objective: (.) Evaluate Logarithmic Epressions 91) ) ID: PCEGU Objective: (.1) Form a Composite domain of f: (-, ); range of f:(, ) horizontal asmptote: = ID: PCEGU6.3.- Objective: (.3) Graph Eponential s 93) 9.1 lb/in. ID: PCEGU Objective: (.3) Define the Number e 9) ln ( - )7 ID: PCEGU6..3- Objective: (.) Write a Logarithmic Epression as a Single Logarithm 9) A ID: PCEGU6..-1 Objective: (.) Graph Logarithmic s 96) log ( + 13) 9 ID: PCEGU6..3- Objective: (.) Write a Logarithmic Epression as a Single Logarithm 97) {11, -11} ID: PCEGU6..-3 Objective: (.) Solve Logarithmic Equations 9) 6 r ID: PCEGU Objective: (.7) Determine the Rate of Interest or Time Required to Double a Lump Sum of Mone 19

20 Answer Ke Testname: FALL FINAL REVIEW ) Yes, es ID: PCEGU Objective: (.1) Form a Composite 0) 6 minutes ID: PCEGU6..3- Objective: (.) Use Newton's Law of Cooling 1) ID: PCEGU Objective: (6.6) Graph Sinusoidal s of the Form = A sin (ω - φ) + B ) amplitude = 0.6, period =, respirator ccle = seconds a a = 0.6sin! t t ID: PCEGU Objective: (6.) Determine the Amplitude and Period of Sinusoidal s 3) 9! 60 ID: PCEGU Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees ) = -3 cos 1 3 ID: PCEGU Objective: (6.) Find an Equation for a Sinusoidal Graph ) integral multiples of! (10 ) ID: PCEGU Objective: (6.3) Determine the Domain and the Range of the Trigonometric s 6)! units to the right ID: PCEGU Objective: (6.6) Graph Sinusoidal s of the Form = A sin (ω - φ) + B 7) cm ID: PCEGU Objective: (6.1) Find the Area of a Sector of a Circle ) 3 3 ID: PCEGU Objective: (6.3) Use Even-Odd Properties to Find the Eact Values of the Trigonometric s 9) - ID: PCEGU Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees 1).9 ft ID: PCEGU Objective: (6.) Graph s of the Form = A csc (ω) + B and = A sec (ω) + B 111) 1 ID: PCEGU Objective: (6.) Find the Eact Values of the Trigonometric s of pi/ = 11) 1 ID: PCEGU Objective: (6.3) Find the Values of the Trigonometric s Using Fundamental Identities 113) 3 ID: PCEGU Objective: (6.6) Graph Sinusoidal s of the Form = A sin (ω - φ) + B 11) ID: PCEGU Objective: (6.3) Find the Values of the Trigonometric s Using Fundamental Identities 11) (i) 1 (ii)! (iii) - 3! ID: PCEGU Objective: (6.6) Graph Sinusoidal s of the Form = A sin (ω - φ) + B 116) = sin 3 + 9! ID: PCEGU Objective: (6.6) Graph Sinusoidal s of the Form = A sin (ω - φ) + B 0

21 Answer Ke Testname: FALL FINAL REVIEW ) m ID: PCEGU Objective: (6.1) Find the Area of a Sector of a Circle 11) 11 ID: PCEGU Objective: (6.) Find the Eact Values of the Trigonometric s of pi/ = 119) ID: PCEGU Objective: (6.3) Use Even-Odd Properties to Find the Eact Values of the Trigonometric s 10) 0 ID: PCEGU Objective: (6.) Find the Eact Values of the Trigonometric s of pi/6 = 30 and pi/3 = 60 11) 0.6 ID: PCEGU Objective: (7.1) Find an Approimate Value of the Inverse Sine, Cosine, and Tangent s 1) = - ID: PCEGU Objective: (7.1) Solve Equations Involving Inverse Trigonometric s 13) not defined ID: PCEGU Objective: (7.1) Use Properties of Inverse s to Find Eact Values of Certain Composite s 1) = 3 ID: PCEGU Objective: (7.1) Solve Equations Involving Inverse Trigonometric s 1) = - 16) 3 3 ID: PCEGU Objective: (7.1) Solve Equations Involving Inverse Trigonometric s ID: PCEGU Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent s 17) ID: PCEGU Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent s 1) 0 ID: PCEGU Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent s 19)! ID: PCEGU Objective: (7.) Define the Inverse Secant, Cosecant, and Cotangent s 130) 131) ID: PCEGU Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent s!, 3!,!, 7! ID: PCEGU Objective: (7.3) Solve Equations Involving a Single Trigonometric 13) θ θ =! + k!, θ = 7! + k! 133) 13) ID: PCEGU Objective: (7.3) Solve Equations Involving a Single Trigonometric 3!, 7!, 11!, and 1! ID: PCEGU Objective: (7.3) Solve Equations Involving a Single Trigonometric!,!,! 3 3 ID: PCEGU Objective: (7.3) Solve Trigonometric Equations Using Fundamental Identities 13) 6.0, 3.3 ID: PCEGU Objective: (7.3) Solve Trigonometric Equations Using a Calculator 1

22 Answer Ke Testname: FALL FINAL REVIEW ) 1 - cot v 1 + cot v + 1 = 1 - cot v csc v + 1 = 1 csc v - cot v csc + 1 v = sin v - cos v sin v 1 sin v + 1 = sin v - cos v + (sin v + cos v) = sin v ID: PCEGU Objective: (7.) Establish Identities 137) (tan v + 1) + (tan v - 1) = tan v + tan v tan v - tan v + 1 = (tan v + 1) = sec v ID: PCEGU Objective: (7.) Establish Identities 13) 1 + csc sec cos sin sin = cos sin + cos = cos + cot. sin ID: PCEGU Objective: (7.) Establish Identities 139) csc + csc - 1 cot ( csc - 1) (csc + 1) (csc - 1) (csc + 1) = cos (sin + 1) sin = = ( csc - 1) (csc + 1) csc = - 1 = csc - 1 csc - 1. ID: PCEGU Objective: (7.) Establish Identities 10) 1 - sin t cos t cos t 1 + sin t. = 1 + sin t 1 + sin t 1 - sin t cos t ID: PCEGU Objective: (7.) Establish Identities = cos t cos t (1 + sin t) =