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Azu Onwe Okwechime (Instructor)HCCS - NORTHWEST COLLEGEPRECALCULUS - MATH 2412 - EXAM # 1 SAMPLE- REVIEW. Exam will consist of 33 to 36 chosen from these QuestionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the distance between the pair of points.1) (5, 4) (-7, -3)A) 193B) 841)C) 5D)95Solve.2) The graph shows an idealized linear relationship for the average monthly payments to retireesfrom 1995 through 1999. Use the midpoint formula to estimate the payment for 1997.2)Average Monthly Payments to 501231995a 452; b 52441997A) 488 dollarsYear1999B) 500 dollarsC) 36 dollarsGraph the circle.3) (x - 4)2 (y - 2)2 93)y105-10-5D) 524 dollars510x-5-101

10y101055-5510x-10-5-5-5-10-10Find the center and radius of the circle.4) x2 y2 - 10x - 12y 52 0A) (6, 5); r 34)B) (-6, -5); r 9C) (-5, -6); r 9Determine the intervals over which the function is decreasing, increasing, and constant.5)y10-1010x-10A) Increasing [3, ); Decreasing [-3, ); Constant (-3, 3)B) Increasing [3, ); Decreasing (- , -3]; Constant [-3, 3]C) Increasing (- , 3]; Decreasing(- , -3]; Constant (-3, 3)D) Increasing (- , 3]; Decreasing [-3, ); Constant [-3, 3]2D) (5, 6); r 35)

Find the average rate of change illustrated in the graph.6)6)3530Value ofCar (inthousandsof dollars)252015105123456YearA) - 3000.00 per yearC) 4000.00 per yearWrite the equation of the line.7) Through (-6, -7)parallel to -2x 7y 26237A) y x 77B) 3000.00 per yearD) - 4000.00 per year7)B) y 626x 77C) y 8) Through (9, -4),perpendicular to -5x - 4y -29456456A) y - x B) y x 555577x 22D) y -237x 778)C) y 34x5D) y 5x - 564

Refer to the following graphs to determine an appropriate response.Graph A4Graph Byy34 x-4x4-3-4Graph CGraph Dyy33-33x4x-39) Which one is the graph of y [[x]]? What is the value of y when x 1.5?A) Graph D; 1B) Graph A; 2.25C) Graph B; 2.2549)D) Graph C; 1

Refer to the following graphs to determine an appropriate response.Graph A4Graph Byy34 x-4x4-3-4Graph CGraph Dyy33-33x4x-310) Which one is the graph of y A) Graph A; (- , )C) Graph C; {-2, -1, 0, 1, 2}x? What is it's domain?B) Graph D; [0, )D) Graph B; [0, )510)

Refer to the following graphs to determine an appropriate response.Graph A4Graph Byy34 x-4x4-3-4Graph CGraph Dyy33-33x4x-311) Which is not the graph of a function? What is its equation?A) Graph C; y x2C) Graph B; x yB) Graph A; y xD) Graph D; y [[x]]611)

Refer to the following graphs to determine an appropriate response.Graph A4Graph Byy34 x-4x4-3-4Graph CGraph Dyy33-33x4x-312) Which one is the graph of y x3? What is its range?A) Graph D; [0, )B) Graph C; [-2, 2]C) Graph B; (- , )D) Graph A; (- , )12)Find the requested value.13)13)6x, if x -1f(-4) for f(x) A) 2x - 2, if x -1B) -24C) 24D) -6Determine if the function is even, odd, or neither.14) f(x) 8x4 7x 5A) Neither15) f(x) -5x3 2xA) Neither14)B) OddC) EvenB) EvenC) Odd15)7

Perform the requested operation or operations.16) f(x) 2x 3, g(x) 16x - 4Find (fg)(x).A) (2x 3)(16x - 4)C) ( 2x 3)( 16x - 4)16)B) (2x 3)(4x - 2)D) (4x - 2)( 2x 3)17) f(x) 9x2 - 7x, g(x) x2 - 3x - 28f(x).FindgA)9x - 7-3B)17)9-x28C)9xx 1D)9x2 - 7xx2 - 3x - 2818) f(x) 4x2 5x 7, g(x) 5x - 3Find (g f)(x).A) 4x2 25x 3219) f(x) 4 - 4x, g(x) -9x 4Find (f g)(x).A) 5x 818)B) 20x2 25x 38C) 20x2 25x 32D) 4x2 5x 419)B) -5xC) -9x 4Find the domain and range of the indicated function.20) Find the domain and range of (fg)(x) when f(x) A) Domain: 2, ; range: (0, )C) Domain: 2, ; range: (- , )Compute and simplify the difference quotientD) -13x 84x 4 and g(x) 3x - 6.B) Domain: - 2, ; range: (- , )D) Domain: 2, ; range: [0, )f(x h) - f(x), h 0.h21) l(x) 6 - 4x3A) -4(3x 2 3xh h2 )21)B) -18x2C) -4(3x 2 - 3x - h)D) -4(x2 - xh - h2)Find the indicated composite for the pair of functions.22) (g f)(x): f(x) 4x2 4x 6, g(x) 4x - 7A) 16x2 16x 3120)22)B) 4x2 16x 17C) 16x2 16x 17D) 4x2 4x - 1Consider the function h as defined. Find functions f and g so that (f g)(x) h(x).23) h(x) 4x 2A) f(x) - x , g(x) 4x 2B) f(x) x, g(x) 4x 2C) f(x) x , g(x) 4x 2D) f(x) -x , g(x) 4x - 223)Solve.24) In a lab experiment 14 grams of acid were produced in 39 minutes and 17 grams in 41 minutes. Lety be the grams produced in x minutes.A) y x 25B) 2y 3x 25C) 2y 3x - 89D) 2y 3x 89824)

Given the equation or other information for a parabola, find the matching description or graph.25) f(x) ax2 bx c,a 0; b2 - 4ac 0A)25)B)5y544332211-5 -4 -3 -2 -1-112345xy-5 -4 -3 -2 -1-1-2-2-3-3-4-4-5-5C)12345x12345xD)5y544332211-5 -4 -3 -2 -1-112345x-5 -4 -3 -2 -1-1-2-2-3-3-4-4-5-5yUse synthetic division to perform the division.x3 - 126)x-1A) x2 x 1 26)1x-1C) x3 x2 x 1 B) x2 x 11x-1D) x3 x2 x 1Express the polynomial in the form P(x) (x - k)Q(x) r for the given value of k.27) P(x) 3x3 - x2 2x 6; k -1A) P(x) (x 1)·(3x2 - 4x 6) 0C) P(x) (x 1)·(3x2 2x) 627)B) P(x) (x - 1)·(3x 2 2x) 6D) P(x) (x 1)·(3x 2 - 4x 2) 8For the polynomial, one zero is given. Find all others.28) P(x) x3 - 3x2 7x - 5; 1A) 1 2i, 1 - 2iB) 1 5i, 1 -28)5iC) 1 5, 1 -5D) -1 2i, -1 - 2iGive all possible rational zeros for the following polynomial.29) P(x) -2x4 2x3 5x2 18A) 1, 1/2, 2, 3, 6, 9, 18C) 1, 2, 3, 6, 9, 1829)B) 1, 2, 1/2, 1/3, 1/6, 1/9, 1/18D) 1, 1/2, 2, 3, 3/2, 6, 9, 9/2, 189

Find all rational zeros and factor f(x).30) f(x) x3 - 7x2 - 4x 2830)A) 3, 8, -2; f(x) (x - 3)(x - 8)(x 2)C) -2, -7, 2; f(x) (x 2)(x 7)(x - 2)B) -3, -8, 2; f(x) (x 3)(x 8)(x - 2)D) 2, 7, -2; f(x) (x - 2)(x - 7)(x 2)Find the zeros of the polynomial function and state the multiplicity of each.31) f(x) 4(x 9)2 (x - 9)331)A) 4, multiplicity 1; 9, multiplicity 1; -9, multiplicity 1B) -9, multiplicity 2; 9, multiplicity 3C) 4, multiplicity 1; -9, multiplicity 3; 9, multiplicity 3D) -9, multiplicity 3; 9, multiplicity 2Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.32) Zeros of -2, 1, 0 and P(2) 16A) P(x) 2x3 2x2 - 4xB) P(x) 2x2 2x - 4C) P(x) 2x3 - 2x2 - 4x32)D) P(x) 2x3 6x2 - 4xFind a polynomial of lowest degree with only real coefficients and having the given zeros.33) 2 i, 4A) f(x) x3 - 8x2 21x - 20B) f(x) x3 9x2 20x 20C) f(x) x3 - 4x2 - (3 - 4i) x 12 16i33)D) f(x) x3 8x2 21x 20Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negativereal zeros for the function.34) 9x8 7x6 4x4 2x2 2 034)A) Positive (4), negative (0)C) Positive (0), negative (4)B) Positive (0), negative (0)D) Positive (4), negative (4)10

Sketch the graph of the rational function.3x35) f(x) (x - 1)(x 4)35)yxA)B)20y401612y328241648-10 -8 -6 -4 -2-42468 10 x-10 -8 -6 -4 -2-8-8-12-16-16-32-4024 68 10 x24 68 10 x-24-20C)D)20y108161264284-10 -8 -6 -4 -2-4y2468 10 x-10 -8 -6 -4 -2-2-4-8-6-12-16-8-10-2011

Use the graph to answer the question.36) Find the horizontal and vertical asymptotes of the rational function graphed below.36)y642-6-4-2246x-2-4-6A) Horizontal: none; vertical: x 3C) Horizontal: y 0; vertical: x 3B) Horizontal: y -4; vertical: x 3D) Horizontal: y 3; vertical: x -4Give the domain and range for the rational function. Use interval notation.137) f(x) 5(x - 3)237)A) Domain: (- , -3) (-3, ); Range: (- , 5)B) Domain: (- , 3) (3, ); Range: (- , 0) (0, )C) Domain: (- , 3) (3, ); Range: (5, )D) Domain: (- , 5) (5, ); Range: (0, )Answer the question38) How can the graph of f(x) 11 7 be obtained from the graph of y ?x-3x38)A) By making a horizontal shift of 7 units to the left and a vertical shift of 3 units downB) By making a horizontal shift of 7 units to the right and a vertical shift of 3 units upC) By making a horizontal shift of 3 units to the left and a vertical shift of 7 units up uupdownD) By making a horizontal shift of 3 units to the right and a vertical shift of 7 units upDetermine which of the rational functions given below has the following feature(s).139) x-intercepts: -1 and -4, y-intercepts: , vertical asymptote: x 4, horizontal asymptote: y 14A) f(x) (x 1)(x 4)(x - 4)2B) f(x) (x - 1)(x - 4)(x 4)C) f(x) (x - 1)(x - 4)(x 4)2D) f(x) (x 1)(x 4)(x - 4)Give the equation of the oblique asymptote, if any.x2 9x - 640) f(x) x-8A) y x 1739)40)B) y x 1C) x y 1712D) None

Write the partial fraction decomposition of the rational expression.x-341)(x - 5)(x - 4)A)2-1 x-5 x-4B)21 x-5 x-4C)2-1 x-5 x-441)D)1-2 x-5 x-4Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for theconstants.3x - 142)42)(x 5)(x 7)2A)ABCD x 5 x 7 x 7 (x 7)2B)ABCDx E x 5 x 7 x 7 (x 7)2C)ABC x 5 x 7 (x 7)2D)ABCx D x 5 x 7 (x 7)213

Answer KeyTestname: PRECALCULUS - EXAM 1 REVIEW - FALL 20101) A2) A3) C4) D5) B6) A7) A8) B9) D10) B11) C12) D13) B14) A15) C16) C17) D18) C19) D20) D21) A22) C23) C24) C25) C26) B27) A28) A29) D30) D31) B32) A33) A34) B35) C36) B37) C38) D39) A40) A41) C42) C14

PRECALCULUS - MATH 2412 - EXAM # 1 SAMPLE- REVIEW. Exam will consist of 33 to 36 chosen from these Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance between the pair of points. 1) (5, 4) (-7, -3) A) 193 B) 84 C) 5 D) 95 1) Solve. 2) The graph shows an idealized linear relationship for the average monthly payments .