SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Practice for the Final Eam MAC 1 Sullivan Version 1 (2007) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (-1, -2); P2 = (6, -3) 1) 2) P1 = (, ); P2 = (, 1) 2) Solve the problem. 3) Find the length of the line segment. 3) Find the midpoint of the line segment joining the points P1 and P2. 4) P1 = (9, 2); P2 = (, 9) 4) ) P1 = (-1, -7); P2 = (3, -4) ) 6) P1 = (0.2, 0.1); P2 = (-1.3, 2.3) 6) List the intercepts for the graph of the equation. 7) = 0 7) List the intercepts of the graph. 8) 8)

2 9) 9) List the intercepts for the graph of the equation. ) 2 = ) 11) = ) Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the origin. 12) 12)

3 13) 13) ) 14) ) 1) Find the center (h, k) and radius r of the circle. Graph the circle. 16) = 0 16) 3

4 Write the standard form of the equation of the circle. 17) 17) (4, ) (8, ) Write the standard form of the equation of the circle with radius r and center (h, k). 18) r = 7; (h, k) = (-1, -4) 18) 19) r = 13; (h, k) = (-, -8) 19) Graph the circle with radius r and center (h, k). 20) r = ; (h, k) = (0, 2) 20) Graph the equation. 21) 2 + ( - )2 = 2 21) Find the center (h, k) and radius r of the circle with the given equation. 22) = 0 22) Find the general form of the equation of the the circle. 23) Center at the point (-4, -3); containing the point (-3, 3) 23) Find the center (h, k) and radius r of the circle with the given equation. 24) = -3 24) Solve the problem. 2) Find an equation of the vertical line containing the point (7, 2). 2) 26) Find an equation of the line with slope undefined and containing the point (- 4, 7). 26) 9 Find the slope-intercept form of the equation of the line with the given properties. 27) horizontal; containing the point (-1, 2) 27) 28) slope = 4; containing the point (-4, -) 28) 4

5 Write the equation in slope-intercept form. 29) = 8 29) 30) + 7 = ) Find the slope and -intercept of the line. 31) 9 - = 90 31) Find the general form of the equation for the line with the given properties. 32) slope = - 6 ; containing the point (4, ) 32) 7 Find an equation for the line with the given properties. 33) Parallel to the line + 2 = 4; containing the point (0, 0) 33) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 34) Parallel to the line = -4-1; containing the point (2, 6) A) = 4-14 B) = 4-26 C) = D) = ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) Perpendicular to the line = 2-1; containing the point (-2, 2) 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a general formula to describe the variation. 36) A varies directl with t2; A = 180 when t = 6 A) A = B) A = 30 t2 t2 C) A = 30t2 D) A = t2 36) 37) The volume V of a right circular cone varies directl with the square of its base radius r and its height h. The constant of proportionalit is 1 3 p. 37) A) V = 1 3 prh B) V = 1 3 pr 2h2 C) V = 1 3 r 2h D) V = 1 3 pr 2h SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 38) On planet X, an object falls 18 feet in 3 seconds. Knowing the distance it falls varies directl with the square of the time of fall, how long does it take an object to fall 0 feet? Round to three decimal places, if necessar. 38) Write a general formula to describe the variation. 39) A varies inversel with 2; A = 4 when = 2 39)

6 Solve the problem. 40) The amount of time Jesse works on his homework each da varies inversel with the amount of time he spends watching TV that da. If he spends 3 hours working on homework when he watches 0. hours of TV, how much time does he spend on homework when he watches 2. hours of TV. 40) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a general formula to describe the variation. 41) z varies jointl as the cube root of and the cube of ; z = 2 when = 12 and = 2. 41) A) z = B) z = C) z = D) z = Solve the problem. 42) The time in hours it takes a satellite to complete an orbit around the earth varies directl as the radius of the orbit (from the center of the earth) and inversel as the orbital velocit. If a satellite completes an orbit 670 miles above the earth in 19 hours at a velocit of 21,000 mph, how long would it take a satellite to complete an orbit if it is at 1600 miles above the earth at a velocit of 24,000 mph? (Use 3960 miles as the radius of the earth.) A).7 hours B) hours C) hours D) 39.7 hours Match the graph to one of the listed functions without using a graphing utilit. 43) 42) 43) A) 2-2 B) C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the verte and ais of smmetr of the graph of the function. 44) f() = ) Solve the problem. 4) Find the point-slope form of the equation of the line containing the points (-3, -1) and (1, -2). Use (-3, -1) as the point (1, 1). Write a general formula to describe the variation. 46) The centrifugal force F of an object speeding around a circular course varies directl as the product of the object's mass m and the square of it's velocit v and inversel as the radius of the turn r. 4) 46) 6

7 Decide whether the pair of lines is parallel, perpendicular, or neither. 47) = = 33 47) Determine whether the relation represents a function. If it is a function, state the domain and range. 48) {(-1, 6), (0, ), (, -4), (6, -1)} 48) Determine whether the equation is a function. 49) 2 = ) Solve the problem. 0) If f() = C and f(-2) = 1, what is the value of C? 0) Find the domain of the function. 1) f() = 21-1) Determine whether the relation represents a function. If it is a function, state the domain and range. 2) Bob Ann Dave carrots peas squash 2) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the equation is a function. 3) = 1 3) A) function B) not a function 4) = ± 1-3 A) function B) not a function 4) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the value for the function. ) Find f() when f() = ) 6) Find f(-) when f() = ) Solve the problem. 7) If f() = - 4A and f(8) = -12, what is the value of A? 7)

8 The graph of a function f is given. Use the graph to answer the question. 8) For what numbers is f() = 0? 8) Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 9) f() = -3( + 1)2-2 9) Find the inverse. Determine whether the inverse represents a function. 60) {(-3, 4), (-1, ), (0, 2), (2, 4), (, 7)} 60) Find the domain of the function. 2 61) g() = ) 62) ) For the given functions f and g, find the requested function and state its domain. 63) f() = 9-4; g() = - 2 Find f - g. 63) 64) f() = + 1; g() = 4-3 Find f g. 64) 8

9 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 6) 6) - - The graph of a function f is given. Use the graph to answer the question. 66) Is f(40) positive or negative? 66) The graph of a function is given. Decide whether it is even, odd, or neither. 67) 67)

10 68) ) Determine algebraicall whether the function is even, odd, or neither. 69) f() = ) 70) f() = 3 70) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 71) (- 3, ) 71) - - Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same aes. 72) f() = )

11 Find the inverse function of f. State the domain and range of f. 73) f() = ) Determine whether the given function is eponential or not. If it is eponential, identif the value of the base a. 74) H() Use transformations to graph the function. Determine the domain, range, and vertical asmptote of the function. 7) Graph the function f() = -1 + e. Determine the domain, range, and horizontal asmptote. 7) 74) Solve the equation. 76) = 26 76) 77) 92 œ 27(3 - ) = ) Change the eponential epression to an equivalent epression involving a logarithm. 78) 321/ = 2 78) Change the logarithmic epression to an equivalent epression involving an eponent. 79) log 8 = 3 79) b Find the eact value of the logarithmic epression. 80) log ) Find the domain of the function. 81) f() = ln (3 - ) 81) Graph the function. 82) f() = -4 ln 82) Solve the equation. 83) log = 3 83) Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. 84) log log ) 8) 2 ln e4.2 8) 11

12 Using the properties of logarithms, find the eact value of the epression. Do not use a calculator. 86) log ) Write as the sum and/or difference of logs. Epress powers as factors ) log 19 q2p 87) Epress as a single logarithm. 88) ( log a t - log a s) + 4 log a u 88) Solve the equation. 89) log 6 (2 + 7) = log 6 (2 + 4) 89) 90) 3( - 1) = 18 90) Solve the problem. 91) Meike earned $16 in tips while working a summer job at a coffee shop. She wants to use this mone to take a trip to Europe net summer. If she places the mone in an account which pas 6.% compounded continuousl, how much mone will she have in nine months? Solve the problem. Round our answer to three decimals. 92) How long will it take for an investment to triple in value if it earns.2% compounded continuousl? 91) 92) Solve the equation. 93) ( 1 4 ) = 13 93) Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to three decimal places. 94) log ) Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. 9) log 6 26 œ log ) Find the eact value of the logarithmic epression. 1 96) log ) 97) log 97) Approimate the value using a calculator. Epress answer rounded to three decimal places. 98) 98) Decide whether or not the functions are inverses of each other. 99) f() = 8-3; g() = ( - 8) 99) 3 12

13 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given functions f and g, find the requested composite function value. 0) Given f() = - 6 and g() = 2 + 9, find (g f)(-2). A) B) 13 C) 2 D) ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The graph of a function f is given. Use the graph to answer the question. 1) Find the numbers, if an, at which f has a local maimum. What are the local maima? ) For the function, find the average rate of change of f from 1 to : f() - f(1), 1-1 2) f() = ) Graph the function. 3) f() = + 4 if < 1-2 if 1 3) 4) f() = if < if 2 4) 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() = ( + 3)3 ) 6) f() = - 6) 13

14 Graph the function using its verte, ais of smmetr, and intercepts. 7) f() = ) Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 8) f() = ) Solve the problem. 9) A projectile is fired from a cliff 400 feet above the water at an inclination of 4e to the horizontal, with a muzzle velocit of 360 feet per second. The height h of the projectile above the water is given b h() = , where is the horizontal distance of the (360)2 projectile from the base of the cliff. Find the maimum height of the projectile. 9) State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 1) f() = ) 111) f() = ) Use transformations of the graph of = 4 or = to graph the function. 112) f() = 3 - ( - 4)4 112) Form a polnomial whose zeros and degree are given. 113) Zeros: 2, multiplicit 2; -2, multiplicit 2; degree 4 113) For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 114) f() = 3( + 7)( + 3)2 114) Find the - and -intercepts of f. 11) f() = ( + 6)( - )( + ) 11) Find the domain of the rational function ) h() = ( + 7)( - 8) 117) h() = ) 117) Give the equation of the specified asmptote(s) ) Vertical asmptote(s): f() = ) 119) Horizontal asmptote: f() = ) 14

15 Find the indicated intercept(s) of the graph of the function. ( - 6)(2 + 7) 120) -intercepts of f() = ) 121) -intercept of f() = ) Give the equation of the specified asmptote(s). 122) Oblique asmptote: f() = ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 123) A can in the shape of a right circular clinder is required to have a volume of 700 cubic centimeters The top and bottom are made up of a material that costs 8É per square centimeter, while the sides are made of material that costs É per square centimeter. Which function below describes the total cost of the material as a function of the radius r of the clinder? A) C(r) = 0.16pr r C) C(r) = 0.08pr r B) C(r) = 0.08pr r D) C(r) = 0.16pr r 123) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the domain of the composite function f g ) f() = ; g() = ) + 6 For the given functions f and g, find the requested composite function value. 12) f() = + 1; g() = ; Find (f g)(1). 12) Decide whether or not the functions are inverses of each other. 126) f() = 8 - ; g() = ( - 8) 126) If the following defines a one-to-one function, find the inverse. 127) f() = ) Approimate the value using a calculator. Epress answer rounded to three decimal places. 128) 4.2 p 128) Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same aes. 129) f() = ) Solve the equation. 130) 130) = 64 1

16 Change the eponential epression to an equivalent epression involving a logarithm. 131) e = ) Find the eact value of the logarithmic epression. 132) log ) Graph the function. 133) = log 2 133) Using the properties of logarithms, find the eact value of the epression. Do not use a calculator. 134) 6 log Solve the equation. 13) Find all real solutions of the following equation. log3 + log3( - 24) = 4 134) 13) 136) 4( - 1) = ) For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 137) f() = 4( - 4)( - 3)2 137) Use the -intercepts to find the intervals on which the graph of f is above and below the -ais. 138) f() = ( )4 ( - 3) 138) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 139) Which of the following polnomial functions might have the graph shown in the illustration below? 139) A) f() = ( - 2)( - 1)2 B) f() = 2( - 2)( - 1) C) f() = ( - 2)2( - 1) D) f() = 2( - 2)2( - 1)2 16

17 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the domain of the rational function ) h() = ) Give the equation of the specified asmptote(s) ) Vertical asmptote(s): f() = ) 142) Horizontal asmptote: h() = ) Solve the sstem of equations b elimination. 143) = = 38 Verif that the values of the variables listed are solutions of the sstem of equations. 144) 3 + = = 8 = -2, = 4 Solve the sstem of equations b elimination. 14) - 2 = = 3 Solve using elimination. 146) = = ) 144) 14) 146) 147) = = ) Graph the inequalit. 148) - > - 148) Graph the sstem of inequalities. 149) ) 17

18 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 1) 2 2) 4 3) 6 4) ( 19 2, 11 2 ) ) (1, ) 6) (-0., 1.2) 7) (0, -1), (-1, 0), (0, 1) 8) (- p 2, 0), (0, 3), (p 2, 0) 9) (-4, 0), (1, 0) (, 0), (0, 4) ) (0, 0) 11) (-4, 0), (0, -3), (0, 3), (4, 0) 12) -ais, -ais, origin 13) none 14) -ais 1) none 16) (h, k) = (1, ); r = ) ( - 6)2 + ( - )2 = 4 18) ( + 1)2 + ( + 4)2 = 49 19) ( + )2 + ( + 8)2 = 13 20)

19 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 21) ) (h, k) = ( 3 2, -2); r = ) = 0 24) (h, k) = (-4, -6); r = 7 2) = 7 26) = ) = 2 28) = ) = ) = ) slope = 9 ; -intercept = -9 32) = 9 33) = ) C 3) = ) D 37) D 38) sec. 39) A = ) 0.6 hours 41) A 42) B 43) C 44) (-2, -1); = -2 4) + 1 = - 1 ( + 3) 4 19

20 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 46) F = kmv 2 r 47) parallel 48) function domain: {-1, 0,, 6} range: {6,, -4, -1} 49) not a function 0) C = - 1) { 21} 2) not a function 3) A 4) B ) - 6) 2 + 7) A = 197 8) -1, 17., 2 9) ) {(4, -3), (, -1), (2, 0), (4, 2), (7, )}; not a function 61) { -7, 7} 62) { > 9} 63) (f - g)() = 4-2; all real numbers 64) ( f + 1 )() = g 4-3 ; { 3 4 } 6) function domain: { -2} range: { 0} intercepts: (-2, 0), (0, -2), (2, 0) smmetr: none 66) negative 67) odd 68) even 69) even 70) odd 71) decreasing 20

21 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 72) ) f -1() = + 2 ; domain of f: { -}; range of f: { 3} 3-74) not eponential 7) domain: (-«, «) range: (-1, «) horizontal asmptote: = -1 76) 3 77) = ) log 32 2 = 1 79) b3 = 8 80) 0 81) < 3 21

22 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 82) ) ) 1 8) ) ) 3 log log 19 q - log 19 p tu4 88) log a s 89) M 90) ) $ ) ears 93) ) ) 2 96) ) 2 98) ) No 0) C 1) f has a local maimum at = 0; the local maimum is 1 1 2)

23 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 3) - - 4) - - )

24 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 6) - - 7) verte (1, 0) intercepts (0, 1), (1, 0) ) maimum; - 7 9) ft 1) Yes; degree 3 111) No; is raised to the negative 6 power 112) ) f() = ) -7, multiplicit 1, crosses -ais; -3, multiplicit 2, touches -ais 11) -intercepts: -6, -, ; -intercept: - 116) { -7, 8} 117) all real numbers 24

25 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 118) = -7, = - 119) = 0 120) (6, 0) and (- 7 2, 0) 121) (0, 4 11 ) 122) = ) A 124) { -1} 12) 6 126) No 127) f-1() = ) ) ) 3, ) ln 14 = 132) ) ) ) = ) ) 4, multiplicit 1, crosses -ais; 3, multiplicit 2, touches -ais 2

26 Answer Ke Testname: MAC1_PRACTICE_2007 (V1) 138) above the -ais: (3, «) below the -ais: (-«, ), (-, 3) ) A 140) { 0, -16} 141) = 7, = ) = 2 143) 144) 14) 146) 147) 148) =, = -3 solution = 3, = 8 = 17, = 19; = - 17, = 19; =, 17, = = 2, = 3; = 2, = -3; = -2, = 3; = -2, = ; = ) , - = 19

C)not a function. B) function domain: {-3, 2, 4, 6} range: {-7, 4, 2, -1}

C)not a function. B) function domain: {-3, 2, 4, 6} range: {-7, 4, 2, -1} Name Spring Semester Final Review (Dual) Precalculus MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation represents a function.