Chapter 2 Test Review


 Rudolph Small
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1 Name Chapter 2 Test Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. 1) f(x) = 8x9 + 6x  7 1) A) Degree: 9; leading coefficient: 8 B) Degree: 9; leading coefficient: 8 2) f(x) = 12x3 + 6x ) A) Degree: 5; leading coefficient: 12 B) Degree: 3; leading coefficient: 12 C) Degree: 12; leading coefficient: 3 D) Not a polynomial function. Write an equation for the linear function f satisfying the given conditions. 3) f(3) = 8 and f(1) = 4 3) A) f(x) =  8 x B) f(x) = 3x + 1 C) f(x) = x + 5 D) f(x) = 3x ) f(1) = 5 and f(5) = 7 4) A) f(x) = 3x  8 B) f(x) = 4x  1 C) f(x) = 3x  8 D) f(x) = 2x  3 Match the equation to the correct graph. 5) y = 2(x + 2)24 5) A) B) C) D) 1
2 6) y = 2(x  3)25 6) A) B) C) D) Determine if the function is a power function. If it is, then state the power and constant of variation. 7) f x = 1 4 x 3 7) A) Power is 1 ; constant of variation is 3 B) Not a power function 4 C) Power is 3; constant of variation is 1 D) Power is 3; constant of variation is 1 4 8) f x = x 2 8) A) Power is 1 7 ; constant of variation is 2 B) Power is 2; constant of variation is C) Not a power function D) Power is 2; constant of variation is 1 7 9) f x = 2x2/7 9) A) Power is ; constant of variation is 2 B) Power is 2 ; constant of variation is 2 7 C) Power is 2; constant of variation is D) Not a power function 10) f x = 2 6x 10) A) Power is 6; constant of variation is 2 B) Power is x; constant of variation is 2 C) Not a power function D) Power is x; constant of variation is 12 2
3 Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. 11) f x = 5 x5 11) A) Degree is 5; leading coefficient is 5 B) Not a monomial function C) Degree is 5; leading coefficient is 5 D) Degree is 5; leading coefficient is 5 12) f x = 7 2x 12) A) Degree is x; leading coefficient is 7 B) Degree is x; leading coefficient is 2 C) Not a monomial function D) Degree is 2; leading coefficient is 7 Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. 13) f x = 3 5 x 4 13) A) Vertically stretch by a factor of 5, and then reflect across xaxis 3 B) Vertically shrink by a factor of 3 5 C) Horizontally shrink by a factor of 3 5 D) Vertically shrink by a factor of 3, and then reflect across xaxis 5 14) f x = 3x5 14) A) Vertically stretch by a factor of 3, and then reflect across xaxis B) Vertically shrink by a factor of 1, and then reflect across xaxis 3 C) Vertically stretch by a factor of 3 D) Horizontally stretch by a factor of 3, and then reflect across xaxis 3
4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given polynomial function. Then sketch the transformed graph. 15) g x =  x ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Describe the end behavior of the polynomial function by finding lim x f x and lim x f x. 16) f x = 4x42x ) A), B), C), D), 17) f x = 2x47x ) A), B), C), D), 18) f x = x34x2 + 6x ) A), B), C), D), Find the zeros of the function. 19) f x = x22x ) A) 5 and 3 B) 5 and 3 C) 5 and 3 D) 5 and 3 20) f x = 3x213x ) A) 4 3 and 3 B) 4 3 and 3 C) 12 and 3 D) and 3 21) f x = 3x3 + 8x2 + 5x 21) A) and 1 B) 0,  5 3, and 1 C) and 1 D) 0,  5, and
5 Divide f(x) by d(x), and write a summary statement in the form indicated. 22) f x = x22x + 3; d x = x  4 (Write answer in polynomial form) 22) A) f x = x B) f x = x C) f x = x  4 x D) f x = x  4 x ) f x = x3 + 5x2 + 8x  5; d x = x + 4 (Write answer in polynomial form) 23) A) f x = x + 4 x2 + x B) f x = x + 4 x2 + x C) f x = x + 4 x2 + x D) f x = x + 4 x2  x ) f x = x22x + 7; d x = x  4 (Write answer in fractional form) 24) f(x) A) x  4 = x f(x) B) x  4 x  4 = x x  4 C) f(x) x  4 = x x  4 D) f(x) x  4 = x x  4 Divide using synthetic division, and write a summary statement in fraction form. 25) 2x 3 + 3x2 + 4x  10 x + 1 A) 2x2 + x x + 1 C) 2x2 + 5x x + 1 B) 2x2 + 5x x + 1 D) 2x2 + x x ) 26) 2x 4  x315x2 + 3x x + 3 A) 2x37x2 + 6x x + 3 C) 2x37x2 + 6x x + 3 B) 2x3 + 5x x + 3 D) 2x35x x ) Find the remainder when f(x) is divided by (x  k) 27) f(x) = 2x3 + 3x2 + 4x + 18; k= 2 27) A) 6 B) 38 C) 10 D) ) f(x) = x28x + 9; k = 8 28) A) 119 B) 137 C) 9 D) 9 29) f(x) = 3x36x24x + 12; k = 2 29) A) 28 B) 16 C) 20 D) 20 5
6 Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. 30) x  4; 2x217x ) A) Yes B) No 31) x  2; 4x212x ) A) Yes B) No Use the Rational Zeros Theorem to write a list of all potential rational zeros 32) f(x) = 2x3 + 7x2 + 8x ) A) ±1, ±2, ±4, ±8 B) ±1, ±1/2, ±1/4, ±1/8, ±2 C) ±1, ±2, ±4 D) ±1, ±1/2, ±2, ±4, ±8 33) f(x) = 2x4 + 5x3 + 2x ) A) ±1, ±1/2, ±2, ±3, ±3/2, ±6, ±9, ±9/2, ±18 B) ±1, ±2, ±1/2, ±1/3, ±1/6, ±1/9, ±1/18 C) ±1, ±1/2, ±2, ±3, ±6, ±9, ±18 D) ±1, ±2, ±3, ±6, ±9, ±18 Find all rational zeros. 34) f(x) = x3 + 2x216x ) A) 2, 4, 4 B) 3, 4, 8 C) 2, 4, 4 D) 3, 4, 8 35) f(x) = 4x312x2  x ) A) 2, 2, 3 B) 1, 1, 3 C) 1 2,  1 2, 3 D) 1 2,  1 2, 3 Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. 36) k = 5; f x = 5x3 + 6x2 + 2x + 4; Upper bound? 36) A) Yes B) No 37) k = 4; f x = 5x35x2 + 4x  4; Upper bound? 37) A) No B) Yes 38) k = 1; f x = 4x34x2 + 3x + 4; Lower bound? 38) A) Yes B) No 39) k = 3; f x = x32x25x + 1; Lower bound? 39) A) Yes B) No 6
7 Use limits to describe the behavior of the rational function near the indicated asymptote. 40) f(x) = 3 x  4 Describe the behavior of the function near its vertical asymptote. A) lim f(x) = , x 4 lim f(x) = B) lim f(x) =, x 4+ x 4 lim f(x) = x ) C) lim f(x) =, x 4 lim f(x) =  D) lim f(x) = , x 4+ x 4 lim f(x) = x 4+ 41) f(x) =  8 x + 2 Describe the behavior of the function near its vertical asymptote. A) lim f(x) =, x 2 lim f(x) =  B) lim f(x) =, x 2+ x 2 lim f(x) =  x 2+ 41) C) lim f(x) = 0, x 2 lim f(x) = 0 D) lim f(x) =, x 2+ x 2 lim f(x) = x 2+ Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f x = 1/x. 42) f x = 1 42) x  5 A) Shift the graph of the reciprocal function up 5 units. B) Shift the graph of the reciprocal function right 5 units. C) Shift the graph of the reciprocal function down 5 units. D) Shift the graph of the reciprocal function left 5 units. 43) f x = 5 x ) A) Shift the graph of the reciprocal function left 4 units, and then stretch vertically by a factor of 5. B) Shift the graph of the reciprocal function left 4 units, and then shrink vertically by a factor of 1 5. C) Shift the graph of the reciprocal function right 4 units, and then stretch vertically by a factor of 5. D) Shift the graph of the reciprocal function left 4 units, and then stretch horizontally by a factor of 5. 7
8 44) f x = 4x  3 x ) A) Shift the graph of the reciprocal function left 3 units, reflect across the xaxis, and then shift 4 units up. B) Shift the graph of the reciprocal function left 3 units, reflect across the xaxis, stretch vertically by a factor of 15, and then shift 4 units down. C) Shift the graph of the reciprocal function left 3 units, reflect across the xaxis, stretch vertically by a factor of 15, and then shift 4 units up. D) Shift the graph of the reciprocal function left 3 units, reflect across the yaxis, stretch vertically by a factor of 15, and then shift 4 units up. 8
9 List the x and yintercepts, and graph the function. 45) f(x) = x  4 x ) A) xintercept: 4, 0 ; yintercept: 0, 4 5 ; B) xintercept: 4, 0 ; yintercept: 0, ; C) xintercept: 4, 0 ; yintercept: 0, ; D) xintercept: 4, 0 ; yintercept: 0, 4 5 ; 9
10 46) f(x) = 2x  3 x ) A) xintercept: xintercept:  5 2, 0, yintercept: 0, B) xintercept: xintercept: 3 2, 0, yintercept: 0,
11 C) xintercept: 5 2, 0, yintercept: 0, D) xintercept:  3 2, 0, yintercept: 0, ) f(x) = x 2  x  12 x ) 11
12 A) xintercepts: (3, 0) and (4, 0), yintercept: (0, 3) ; B) xintercepts: (3, 0) and (4, 0), yintercept: (0,  3) ; C) xintercepts: (3, 0) and (4, 0), yintercept: (0, 12) ; D) xintercepts: (3, 0) and (4, 0), yintercept: (0, 12) ; For the given function, find all asymptotes of the type indicated (if there are any) 48) f(x) = x  9, vertical 48) x2 + 9 A) None B) x = 9 C) x = 9 D) x = 3, x = 3 49) f(x) = x 2 + 9x  2, slant 49) x  5 A) y = x + 4 B) None C) x = y + 14 D) y = x ) f(x) = 2x 2 + 2, horizontal 50) 2x22 A) y = 2 B) y = 2 C) None D) y = 1 Solve the equation. 51) x + 1 = 2 x 51) A) x = ± 2 B) x = 1 C) x = 1 or x = 2 D) x = 2 or x = 1 12
13 52) 9x x x = 36 x29x 52) A) x = 9 4 B) x = 2 9 or C) x = 4 9 or D) x = ) x 2x + 2 = 2x 4x x  3 x + 1 A) x = 3 2 B) x = 3 C) x = 3 D) x = ) Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. 54) f x = x + 4 x + 1 x ) A) (a) 4, 1, 2, (b), 41, 2, (c) 4, 1 2, B) (a) 4, 1, 2, (b) 4, 1 2,, (c), 41, 2 C) (a) 4, 1, 2, (b) 4, 2, (c), 4 2, D) (a) 4, 1, 2, (b) 4, 1 2,, (c), 41, 2 55) f x = 2x2 + 6 x x ) A) (a) 9, 6, (b) 9,, (c), 9 B) (a) 9, 6, (b) 9, 6 (6, ) (c), 9 C) (a) 9, 6, (b) 9, 6 (c) 9, (6, ) D) (a) 9, 6, (b) 6,, (c), 6 Solve the polynomial inequality. 56) (x + 7)(x + 6)(x + 2) > 0 56) A) (2, ) B) (7, 6) (2, ) C) (, 6) D) (, 7) (6, 2) 57) 2x + 3 x  4 3x ) A) 3/2, 2/3 4, B) 3/2, 2/3 4, C), 3/2 2/3, 4 D), 3/2 2/3, 4 Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. x ) f x = 2x + 3 x ) A) (a) 7, (b) 7, 3/2, (c), 3/2 4, 7, (d) 3/2, 4 7, B) (a) 4, 7, (b) 3/2, (c) 3/2, 4 7,, (d), 3/2 4, 7 C) (a) 4, 7, 3/2, (b), (c), 3/2 4, 7, (d) 3/2, 4 7, D) (a) 4, (b) 7, 3/2, (c) 3/2, 4 7,, (d), 3/2 4, 7 13
14 59) f x = x  4 x  7 x ) A) (a) 4, (b) 7, 8, (c) 8, 4 7,, (d) 4, 7 B) (a) 4, 7, (b), 8, (c) 8, 4 7,, (d) 4, 7 C) (a) 4, 7, (b), 8, (c) 4, 7, (d) 8, 4 7, D) (a) 4, (b) 7, 8, (c) 4, 7, (d) 8, 4 7, Solve the inequality. 60) x  2 x2 0 60) A) [2, 0) 0, 1 3 C) B) 2, 1 3, 2 D) (, 2] 1 3,
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