Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Final Eam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) ) Does the table define as a function of? A) Yes B) No Use the table to answer the question. ) = f() ) Is f(16) an input or output of this function? A) Input B) Output 3) = g() ) Is 30 an input or output of this function? A) Input B) Output Evaluate the function. 4) ) If = f(), find f(-). A) -1 B) 4 C) 1 D) -4 1

2 State whether the graph is or is not that of a function. 5) 10 5) A) Yes B) No Decide whether or not the arrow diagram defines a function. 6) Domain Range 6) A) Yes B) No 7) Domain Range 7) A) No B) Yes 8) Domain Range 8) A) No B) Yes Find the domain and range for the function. 9) ) A) D: [0, 5]; R: [-, 5] B) D: [-, 5]; R: [0, 5] C) D: (-, 5); R: (0, 5) D) D: [, 5]; R: [0, 5]

3 Find the domain of the function. 10) = 8 + A) (-, -8 B) [-8, ) C) [0, ) D) (-, ) 11) = A) all real numbers ecept 8 B) (8, ) C) (-, 8) D) all real numbers ecept -8 10) 11) Provide an appropriate response. 1) If the ordered pair (, 4) belongs to function g, then g( ) =. A) ; B) ; 4 C) 4; D) ; 4 1) Solve the problem. 13) A small to compan that onl makes action figures is owned b its stockholders. The dividend per share of stock is a function of the number of action figures it sells and is defined b D() = $4.43-$70, where is the number of action figures sold. What is the dividend for each 3936 share of stock if 1350 action figures are sold? A) -$1.45 B) $1.45 C) -$68.48 D) $ ) Suppose the sales of a particular brand of appliance are modeled b the linear function S() = , where S() represents the number of sales in ear, with = 0 corresponding to 00. Use this model to predict the number of sales in 018. A) 450 sales B) 8640 sales C) 8570 sales D) 430 sales 13) 14) Find the slope of the line through the pair of points. 15) (8, -7) and (-1, 3) A) B) 9 10 C) D) ) Find the slope of the line. 16) 16) A) 0 B) -4 C) undefined D) 4 3

4 Decide whether the slope is positive, negative, zero, or undefined. 17) 10 17) A) Zero B) Negative C) Positive D) Undefined Find the slope of the line (if it eists) and the -intercept (if it eists). 18) = A) Slope -6; -intercept (0, 7) B) Slope -7; -intercept (0, 6) C) Slope 7; -intercept (0, 6) D) Slope 6; -intercept (0, 7) 18) Solve the problem. 19) A boat is moving awa from shore in such a wa that at time t hours its distance from shore, in kilometers, is given b the linear function d(t) = 3.5t What is the rate of change of the distance from shore? A) 6.1 km/hr B) 3.5 m/s C) 6.1 m/s D) 3.5 km/hr 19) Use the data shown in the scatter plot to determine whether the data should be modeled b a linear function. 0) 0) A) Yes, approimatel linear B) No, data points do not lie close to a line C) Yes, eactl linear 4

5 1) 1) A) Yes, eactl linear B) No, data points do not lie close to a line C) Yes, approimatel linear Write the best-fit linear model for the data. ) Ten students in a graduate program were randoml selected. Their grade point averages (GPAs) when the entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Find a linear function that predicts a studentʹs current GPA as a function of his or her entering GPA. ) Entering GPA Current GPA A) = B) = C) = D) = Does the sstem have a unique solution, no solution, or man solutions? 3) - = = -18 A) A unique solution B) Man solutions C) No solution 3) Solve the sstem of equations b substitution, if a solution eists. 4) = = -6 A) No solution B) = -7, = 5 C) = -6, = 4 D) = -6, = 5 4) 5) + = 8 + = 7 A) = 7, = 8 B) = 8, = 7 C) = 0, = 15 D) No solution 5) Solve the sstem of equations b elimination, if a solution eists. 6) = 6 - = -4 A) = 6, = 9 B) = 6, = 8 C) = 5, = 9 D) No solution 6) 5

6 Solve the sstem. - + z = 8 7) + + z = z = -1 A) =, = -1, z = -9 B) = -, = -1, z = 9 C) = -, = -1, z = -9 D) =, = -1, z = 9 7) 8) - + 3z = -8 + z = z = 40 A) = -8, = 0, z = 0 B) = 8, = 8, z = 0 C) = 0, = -8, z = -8 D) = 0, = 8, z = 0 8) Solve the problem. 9) Suppose that the total annual consumption of salmon in a certain countr is given b = and that the total annual consumption of tuna in this countr is given b = , where consumption is measured in millions of pounds and is the number of ears since 010. Find the ear in which consumption of salmon reaches consumption of tuna. A) 00 B) 019 C) 017 D) 015 9) To find the number of units that gives break-even for the product, solve the equation R = C. Round our answer to the nearest whole unit. 30) A manufacturer has total revenue given b the function R = 70 and has total cost given b 30) C = ,000, where is the number of units produced and sold. A) 89 units B) 5350 units C) 10 units D) 0 units Solve the inequalit and draw a number line graph of the solution. 31) > ) A) a > B) a > C) a < D) a <

7 Solve the double inequalit. 3) -4 < A) - 9 < 33 C) 9 < < 33 B) 9 < 33 D) ) Use the graph of the function to estimate the -intercepts. 33) = ) A) = -5, = 7 B) = 5, = 7 C) = -7, = 5 D) = -35, = - Use factoring to solve the equation. 34) k - 7k - 4 = 0 A) 1 7, - 1 B) - 1, 4 C) -, 4 D) - 1, 34) Use the square root method to solve the equation. 35) 4 = 60 A) 30 B) 16 C) ± 15 D) ±15 35) Solve the equation b completing the square. 36) q + 4q - 7 = 0 A) + 11 B) - ± 11 C) -1 ± 11 D) - ± 11 36) Use the quadratic formula to solve the equation. 37) = 0 A) -4, -5 B) 4, 5 C) 5, 4, 5 D) 0, 4, 5 37) Find the eact solutions to the quadratic equation in the comple numbers. 38) = 0 A) -1 ± i 35 B) 1 ± 35 C) -1 ± 35 D) 1 ± i 35 38) 7

8 Find the requested value. 39) 5, if -1 f(-) for f() = - 7, if > -1 A) -5 B) -10 C) 10 D) -9 40) if 0 f(5) for f() = 4-4 if 0 < < 4 if 4 A) 4 B) 4 C) 5 D) ) 40) Solve the equation. 41) 6m + = 7 41) A) 5, - 9 B) 5 6, - 3 C) - 5 6, 3 D) 5 6 Provide an appropriate response. 4) Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient of should be positive or negative. 4) DENTAL FLOSS USE 10 People (in Millions) Years since 000 A) Quadratic; negative B) Quadratic; positive C) Linear; positive D) Linear; negative Fill in each blank with the appropriate response. 43) The graph of = can be obtained from the graph of = b shifting horizontall units to the, and shifting verticall units in the direction. A) 3; right; 4 downward B) 4; right; 3; upward C) 3; right; 4; upward D) 4; left; 3; upward 43) 8

9 Write the equation of the graph after the indicated transformation(s). 44) The graph of = is shifted units to the left. This graph is then verticall stretched b a factor of 6 and reflected across the -ais. Finall, the graph is shifted 7 units downward. A) = -6( + 7) - B) = -6( - ) + 7 C) = -6( + ) - 7 D) = -6( - ) ) Write the equation of the function g() that is transformed from the given function f(), and whose graph is shown. 45) f() = 45) A) = ( - 3) - 3 B) = ( + 3) C) = ( - ) - 3 D) = -( - 3) For the pair of functions, perform the indicated operation. 46) f() = 3-3, g() = Find (f + g)(). A) -3 B) C) D) ) Evaluate. 47) If f() = 3 f and g() = - 3, evaluate g (3). A) 7 B) 1 C) 0 D) Undefined 47) Find the requested function value. 48) Find (g f)(7) when f() = and g() = A) 335 B) 83 C) -487 D) 59 48) Determine if the function is a growth eponential or a deca eponential. 49) = 7e -3 A) Growth B) Deca 49) Find the function value. 50) Let f() = 1 5. Find f(-3). 50) A) 15 B) C) 1 15 D) -15 Write in logarithmic form. 51) 10 = 100 A) log 100 = 10 B) log 10 = 100 C) log = D) log 10 = ) 9

10 Find the value of the logarithm without using a calculator. 1 5) log 9 79 A) 81 B) -81 C) 3 D) -3 5) Find the inverse of the function. 53) f() = 7 A) f -1 () = 7 B) f -1 () = ln(7) C) f -1 () = log 7 D) f -1 () = log7 53) Rewrite the epression as the sum and/or difference of logarithms, without using eponents. Simplif if possible. 54) log sr 54) A) 1 10 log log 9 s - log 9 r B) log log 9 s - log 9 r C) 10 log log 9 s - log 9 10 D) 1 10 log log 9 s - log 9 r Rewrite as a single logarithm. 55) 3 log 6 (5-1) + log 6 ( + 8) 55) A) log 6 ((5-1) 3 + ( + 8) ) B) log 6 (5-1) 3 ( + 8) (5-1)3 C) 6 log 6 (5-1)( + 8) D) log 6 ( + 8) Use a change of base formula to evaluate the given logarithm. Approimate to three decimal places. 56) log 6 (95.63) A) B) C).545 D) ) Solve the equation. 57) 3 (4 - ) = Round to three decimal places. A) B) 0.03 C) 1.03 D) ) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 58) e + 5 = A) {e + 5} B) {ln 7} C) {ln - 5} D) {e 10 } 58) Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. 59) ln = 7 59) A) ln 3 B) e /3 C) e 3 D) 3 ln 1 10

11 60) log (4 + ) - log ( - 4) = log 3 A) {8} B) 3 C) D) {-8} 60) Solve the equation. Give an eact solution. 61) log9( - 3) + log9( - 3) = 1 A) -6, 6 B) 6 C) - 10, 10 D) 10 61) Provide an appropriate response. 6) Select an appropriate tpe of modeling function for the data shown in the graph. Choose from eponential, logarithmic, and linear. 6) A) Linear B) Eponential C) Logarithmic Solve the problem. 63) Find out how long it takes a $3100 investment to double if it is invested at 8% compounded 63) semiannuall. Round to the nearest tenth of a ear. Use the formula A = P 1 + r n nt. A) 9 ears B) 9. ears C) 8.6 ears D) 8.8 ears 64) The formula A = 00e 0.033t models the population of a particular cit, in thousands, t ears after When will the population of the cit reach 97 thousand? A) 011 B) 013 C) 010 D) 01 64) 65) The number of students infected with the flu on a college campus after t das is modeled b the 40 function P(t) =. What was the initial number of infected students? e-0.3t A) 1 students B) 6 students C) 40 students D) 39 students 66) In how man was can 7 plaers be assigned to 7 positions on a baseball team, assuming that an plaer can pla an position? A) 5040 was B) 4 was C) 50 was D) 10,080 was 65) 66) 11

12 67) A restaurant offers a choice of 5 salads, 7 main courses, and 4 desserts. How man possible 3-course meals are there? A) 35 possible meals B) 140 possible meals C) 80 possible meals D) 16 possible meals 67) Use the formula for n P r to evaluate the epression. 68) 7 P 3 A) 10 B) 1680 C) 840 D) ) Solve the problem. 69) How man 3-letter codes can be formed using the letters A, B, C, D, and E? No letter can be used more than once. A) 40 B) 60 C) 0 D) 10 69) Use the formula for n C r to evaluate the epression. 70) 11 C 5 A) 33,640 B) 7,983,360 C) 55,440 D) 46 70) 1

13 Answer Ke Testname: FINAL EXAM REVIEW 1) B ) B 3) A 4) C 5) B 6) B 7) B 8) B 9) B 10) B 11) A 1) D 13) B 14) D 15) A 16) C 17) B 18) D 19) D 0) B 1) C ) C 3) C 4) C 5) D 6) B 7) B 8) D 9) C 30) B 31) A 3) A 33) A 34) B 35) C 36) D 37) B 38) A 39) B 40) C 41) B 4) A 43) B 44) C 45) A 46) C 47) D 48) C 49) B 50) A 13

14 Answer Ke Testname: FINAL EXAM REVIEW 51) C 5) D 53) D 54) D 55) B 56) C 57) C 58) C 59) B 60) A 61) B 6) B 63) D 64) C 65) B 66) A 67) B 68) A 69) B 70) D 14

M122 College Algebra Review for Final Exam

M122 College Algebra Review for Final Exam M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra - Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature