Name: Class: Date: Rationals Multiple Choice Post-Test
Name:Class: Date:Rationals Multiple Choice Post-TestMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1 Which family of functions does y A TrigonometricB Logarithmic4belong to?x2C ExponentialD Rational2 Which of the following functions is not rational?1xx 4f(x) x 83xx 5x2 1f(x) 2x 2x 1A f(x) C f(x) BD3 Simplify the expression and state the excluded values:A p 8; p 4B p 8; p 4p 2 4p 32p 4C p 8; p 4D p 8; p 4.
4 Multiply. State the excluded values:ABz 3z 2z 35 Simplify:ABz 2 2z, z 1, 0, 3a 8 72a 64z 1 z 2 3z 2z 2 3zC, z 1, 37z2Dz 2z 3., z 1, 3z 2 2zz 3, z 1, 0, 3.7a 49(a 8)(a 8)142a a 566 Given the graph of the function f(x) C14(a 8)(a 8)D7a 63(a 8)(a 8)1. Which of the following represents the behavior of the functionx2as x approaches negative infinity?A approaches negative infinityB approaches zeroAlgebra II Rationals Post-TestC approaches positive infinityD approaches onePage 2
7 Describe the vertical asymptote(s) and hole(s) for the graph of y (x 5)(x 2)(x 2)(x 4).A asymptote: x –4 and hole: x 2C asymptote: x –5 and hole: x –4BD asymptote: x 4 and hole: x –2asymptotes: x –4 and x 28 If R is the total resistance for a parallel circuit with two resistors of resistances r 1 and r 2 , then1R1 r1 1r2. Find the resistance r 1 if the total resistance R is 20 ohms and r 2 is 75 ohms. Round youranswer to the nearest ohm if necessary.A 16 ohmsC 27 ohmsBD 102 ohms1405 ohms9 Solve the equation for x:A B 2x 4 4x 3.136D 1110 Solve the equation for w:3141168311 3C 56w 1w 4.112431 24A C BDAlgebra II Rationals Post-TestPage 3
11 A group of high school students are volunteering for Habitat for Humanity during their summer break.They are putting the finishing touches on a house they built. Working alone, Kendra can paint a certainroom in 7 hours. Joe can paint the same room in 6 hours. Write an equation that can be used to find howlong it will take them working together to paint the room. How many hours will it take them to paint theroom? If necessary, round your answer to the nearest tenth.7 61 11A 1; 13 hoursC ; 6.5 hoursx x7 6xx xx x 1; 3.2 hours 1; 6.5 hoursBD7 66 712 Sketch the asymptotes and graph the function.y x 2 7x 12x2 1ACBDAlgebra II Rationals Post-TestPage 4
13 State the domain of the function y ABB x x 9,x 7 x x 9,x 7 14 Simplify the following expression:A(x 6)(x 2)(x 8).(x 9)(x 7)(x 2)(x 5)x 4(x 2)(x 4)CDx 2x 1 x 42x 4x 5, x 5, 4C, x 1, 5D(x 1) 2 (x 5) x x 6,x 2,x 8 x x ℜ (x 2)(x 4), x 1, 5, 4(x 1) 2 (x 5)(x 2)(x 5);x 1, 4, 5x 415 Determine the horizontal asymptote of the function. y Ay 3By C y 13.6x 2 1.2x 2 313D y 316 Which function does not have a horizontal asymptote.A g(x) x 6x2 2x2g(x) 3x 2 1C g(x) x 9x 3BD g(x) x3 26x 2 5Algebra II Rationals Post-TestPage 5
17 Reduce the fraction to lowest terms:8x 2 4x.2xC 2x 2 1A 2x 1B4x 2 218 Solve the equationD 4x 2114 2for x.x 2 x 2 x 4A x 1B x 419 Find the x-intercept of the function: h(x) A (-1,0)B (1,0)Algebra II Rationals Post-TestC No solutionD x 2x 2 2x 1.x2 1C (0,1)D there is no x-interceptPage 6
20 Solve for y, then graph the function.xy 16 0ACBD21 Describe the vertical asymptote(s) and hole(s) for the graph of y (x 5)(x 2)(x 2)(x 4).A asymptote: x - 4 and hole: x 2C asymptote: x - 5 and hole: x -4BD asymptote: x 4 and hole: x -2asymptotes: x - 4 and x -2Algebra II Rationals Post-TestPage 7
22Which equation best represents the graph?A y (x 2)(x 4)C y (x 4)(x 2)B(x 2)(x 4)D y (x 2)(x 4)y 23 Describe the holes for the graph of the rational function y (x 2).(x 2)(x 5)A Hole: x –2C Hole: x – 5BD Hole: x 5Hole: x 2Algebra II Rationals Post-TestPage 8
24 What are the x and y-intercepts of the rational function R(x) A x-intecepts: (4, 0) and (-3, 0)C x-intecepts: (4, 0) and (-3, 0)y-intercept: (0, –2)Bx-intecepts: (-4, 0) and (3, 0)1y-intercept: (0, 6 )x 2 x 12?x 6y-intercept: (0, 2)D x-intecepts: (-4, 0) and (3, 0)y-intercept: (0, -2)25 Find any points of discontinuity for the rational function: y (x 6)(x 2)(x 8)(x 9)(x 7)Ax 6 x 2, x 8CBx 9, x 7D x -6, x -2, x -8.x -9, x -726 What are the vertical and horizontal asymptotes of the rational function?y A Vertical Asymptotes: x 2Horizontal Asymptotes y 3BVertical Asymptotes: x 2Horizontal Asymptotes y –3Algebra II Rationals Post-Test1x 2 3C Vertical Asymptotes: x –2Horizontal Asymptotes y –3D Vertical Asymptotes: x –2Horizontal Asymptotes y 3Page 9
27 Determine the end behavior of the function.f(x) (2x 4)(2x 2 1)A As the x-values approach negativeinfinity, the graph approaches thehorizontal asymptote from below. Asthe x-values approach positiveinfinity, the graph approaches thehorizontal asymptote from above.C As the x-values approach negativeinfinity, the graph approaches thevertical asymptote from below. As thex-values approach positive infinity,the graph approaches the horizontalasymptote from above.BD As the x-values approach negativeinfinity, the graph approaches thehorizontal asymptote from above. Asthe x-values approach positiveinfinity, the graph approaches thehorizontal asymptote from above.As the x-values approach negativeinfinity, the graph approaches thehorizontal asymptote from below. Asthe x-values approach positiveinfinity, the graph approaches thehorizontal asymptote from below.28 Determine the horizontal asymptotes of the function: g(x) x2 1.x 2A Horizontal asymptote: y –1C Horizontal asymptote: y 1/2BD There is no horizontal asymptoteHorizontal asymptote: y 2Algebra II Rationals Post-TestPage 10
29 Simplify the following rational expression, state any excluded values.2x4x 2x x 2 x 3x 22A 2x 2 6x,x 1,x 2(x 2)(x 1)(x 1)C 2x 2 2x,x 1,x 2(x 2)(x 1)(x 1)B6x 2 2x,x 1,x 2(x 2)(x 1)(x 1)D6x 2 6x,x 1,x 2(x 2)(x 1)(x 1)30 Simplify the following rational expression, state any excluded values.47 x 9 x 32AB7x 25,x 3x2 97x 17,x 3x2 9CD 7x 25,x 3x2 9 7x 17,x 3x2 931 Simplify the following rational expression, state any excluded values.x 3 5x 2 6x x 2 3x 2 2x2 4x 2x 3x(x 2),x 2,x 3,x 1(x 2)A 1CBD x, no restrictionsx, x 2,x 3,x 132 Simplify the following rational expression, state any excluded values.x 2 5x 6 x 2 3x 10 x34x 2AB8(x 3)' x 5,x 0,x 23(x 5)(x 2 5x 6)(x 2 3x 10)Algebra II Rationals Post-Test4x5,x 0C4(x 3)(x 2)' x 5,x 0,x 2x(x 5)(x 2)D4(x 3)' x 5,x 0,x 2x(x 5)Page 11
1x33 Write the equation of the parent function f(x) , after a translation of 3 to the left and 5 down.AB1 5x 31f(x) 5x 3f(x) CD1 5x 31f(x) 5x 3f(x) 1x34 The graph below is a transformation of the parent function f(x) . Write the equation of the graph.AB1 5x 11f(x) 5x 1f(x) Algebra II Rationals Post-TestCD 1 5x 1 1f(x) 5x 1f(x) Page 12
Algebra II Rationals Post-Test Page 3 _ 7 Describe the vertical asymptote(s) and hole(s) for the graph of y (x 5)(x 2)(x 2)(x 4)A asymptote: x –4 and hole: x 2 C asymptote: x –5 and hole: x –4 B asymptotes: x –4 and x 2 D asymptote: x 4 and hole: x –2 _ 8 If R is the total resistance for a parallel circuit with two resistors of resistances r1 and .
3. Ordering the rational numbers 8 4. Sequences and limits in Q 11 5. Non-convergent Cauchy sequences of rationals 13 5.1. An irrational sequence of rationals 13 5.2. An irrational sequence in Qthat is not algebraic 15 6. Extending Qto the real and complex numbers: a summary 17 6.1. The real numbers R 17 6.2. The complex numbers C 19 1. The Set Q
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