Name: Class: Date: Rationals Multiple Choice Post-Test. Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Name: _ Class: _ Date: Rationals Multiple Choice Post-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Which family of functions does y = 4 belong to? 2 x Trigonometric C Exponential Logarithmic D Rational 2 Which of the following functions is not rational? f(x) = 1 x f(x) = x 4 x + 8 C f(x) = D f(x) = 3x x + 5 x 2 1 x 2 + 2x Simplify the expression and state the excluded values: p 2 4p 32. p + 4 p + 8; p 4 C p 8; p 4 p 8; p 4 D p + 8; p 4

2 4 Multiply. State the excluded values: z 2 z + 1 z 2 + 3z + 2. z 2 + 3z z2 + 2z z + 3, z 1, 3 C z + 2 z + 3, z 1, 3 z + 2 z + 3 z 2 + 2z, z 1, 0, 3 D z + 3, z 1, 0, 3 5 Simplify: 7 a a a 49 (a 8)(a + 8) 14 a 2 + a 56 C D 14 (a 8)(a + 8) 7a + 63 (a 8)(a + 8) 6 Given the graph of the function f(x) = 1. Which of the following represents the behavior of the function 2 x as x approaches negative infinity? approaches negative infinity C approaches positive infinity approaches zero D approaches one lgebra II Rationals Post-Test Page 2

3 7 Describe the vertical asymptote(s) and hole(s) for the graph of y = (x 5)(x 2) (x 2)(x + 4). asymptote: x = 4 and hole: x = 2 C asymptote: x = 5 and hole: x = 4 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 r 1 and r 2, then 1 R = Find the resistance r 1 if the total resistance R is 20 ohms and r 2 is 75 ohms. Round your r 1 r 2 answer to the nearest ohm if necessary. 16 ohms C 27 ohms 1405 ohms D 102 ohms 9 Solve the equation for x: 2 x + 4 = 4 x C D Solve the equation for w: 5 6w + 1 w = C D lgebra II Rationals Post-Test Page 3

4 11 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 certain room in 7 hours. Joe can paint the same room in 6 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest tenth. 7 x + 6 x = 1; 13 hours C = 1 ; 6.5 hours x x 7 + x 6 = 1; 3.2 hours D x 6 + x 7 = 1; 6.5 hours 12 Sketch the asymptotes and graph the function. y = x 2 7x + 12 x 2 1 C D lgebra II Rationals Post-Test Page 4

5 13 State the domain of the function y = (x + 6)(x + 2)(x + 8). (x + 9)(x + 7) x x 9,x 7 C x x 6,x 2,x 8 x x 9,x 7 D x x R 14 Simplify the following expression: x + 2 x 1 x + 4 x 2 + 4x 5. (x + 2)(x + 5) (x + 2)(x + 4), x 5, 4 C, x 1, 5, 4 x + 4 (x 1) 2 (x + 5) (x + 2)(x + 4) (x + 2)(x + 5), x 1, 5 D ;x 1, 4, 5 (x 1) 2 (x + 5) x Determine the horizontal asymptote of the function. y = 6x x 2 3. y = 3 C y = 1 3 y = 1 3 D y = 3 16 Which function does not have a horizontal asymptote. g(x) = x 6 x g(x) = x 2 3x C g(x) = x 9 x + 3 D g(x) = x 3 2 6x 2 5 lgebra II Rationals Post-Test Page 5

6 17 Reduce the fraction to lowest terms: 8x 2 + 4x. 2x 2x + 1 C 2x x D 4x Solve the equation 1 x x 2 = 4 for x. x 2 4 x = 1 C No solution x = 4 D x = 2 19 Find the x-intercept of the function: h(x) = x 2 2x + 1. x 2 1 (-1,0) C (0,1) (1,0) D there is no x-intercept lgebra II Rationals Post-Test Page 6

7 20 Solve for y, then graph the function. xy + 16 = 0 C D 21 Describe the vertical asymptote(s) and hole(s) for the graph of y = (x 5)(x 2) (x 2)(x + 4). asymptote: x = - 4 and hole: x = 2 C asymptote: x = - 5 and hole: x = -4 asymptotes: x = - 4 and x = -2 D asymptote: x = 4 and hole: x = -2 lgebra II Rationals Post-Test Page 7

8 22 Which equation best represents the graph? y = (x 2) (x 4) (x + 2) y = (x + 4) (x + 4) C y = (x 2) (x + 2) D y = (x 4) 23 Describe the holes for the graph of the rational function y = (x 2) (x 2)(x + 5). Hole: x = 2 C Hole: x = 5 Hole: x = 2 D Hole: x = 5 lgebra II Rationals Post-Test Page 8

9 24 What are the x and y-intercepts of the rational function R(x) = x 2 x 12? x + 6 x-intecepts: (4, 0) and (-3, 0) y-intercept: (0, 2) C x-intecepts: (4, 0) and (-3, 0) y-intercept: (0, 2) x-intecepts: (-4, 0) and (3, 0) D x-intecepts: (-4, 0) and (3, 0) y-intercept: (0, 1 ) y-intercept: (0, -2) 6 25 Find any points of discontinuity for the rational function: y = (x + 6)(x + 2)(x + 8). (x + 9)(x + 7) x =6 x =2, x = 8 C x = -9, x = -7 x = 9, x = 7 D x = -6, x = -2, x = What are the vertical and horizontal asymptotes of the rational function? 1 y = x Vertical symptotes: x = 2 Horizontal symptotes y = 3 Vertical symptotes: x = 2 Horizontal symptotes y = 3 C Vertical symptotes: x = 2 Horizontal symptotes y = 3 D Vertical symptotes: x = 2 Horizontal symptotes y = 3 lgebra II Rationals Post-Test Page 9

10 27 Determine the end behavior of the function. f(x) = (2x 4) (2x 2 1) s the x-values approach negative horizontal asymptote from below. s the x-values approach positive horizontal asymptote from above. C s the x-values approach negative vertical asymptote from below. s the x-values approach positive infinity, the graph approaches the horizontal asymptote from above. s the x-values approach negative horizontal asymptote from below. s the x-values approach positive horizontal asymptote from below. D s the x-values approach negative horizontal asymptote from above. s the x-values approach positive horizontal asymptote from above. 28 Determine the horizontal asymptotes of the function: g(x) = x x 2. Horizontal asymptote: y = 1 C Horizontal asymptote: y = 1/2 Horizontal asymptote: y = 2 D There is no horizontal asymptote lgebra II Rationals Post-Test Page 10

11 29 Simplify the following rational expression, state any excluded values. 2x x 2 x 2 4x x 2 3x + 2 2x 2 6x (x 2)(x + 1)(x 1),x ±1,x 2 C 2x 2 + 2x,x ±1,x 2 (x 2)(x + 1)(x 1) 6x 2 + 2x (x 2)(x + 1)(x 1),x ±1,x 2 D 6x 2 6x,x ±1,x 2 (x 2)(x + 1)(x 1) 30 Simplify the following rational expression, state any excluded values. 4 x x + 3 7x + 25 x 2 9 7x 17 x 2 9,x ±3 C 7x + 25 x 2 9,x ±3 D 7x 17 x 2 9,x ±3,x ±3 31 Simplify the following rational expression, state any excluded values.. x 3 5x 2 + 6x x 2 4 x 2 + 3x + 2 x 2 2x 3 1 C x(x 2) (x + 2) x, x ±2,x 3,x 1 D x, no restrictions,x ±2,x 3,x 1 32 Simplify the following rational expression, state any excluded values.. x 2 5x + 6 x 2 + 3x 10 x 3 4x 2 8(x 3) 4(x 3)(x + 2) ' x 5,x 0,x 2 C ' x 5,x 0,x 2 3(x + 5) x(x + 5)(x 2) (x 2 5x + 6)(x 2 + 3x 10) 4x 5,x 0 D 4(x 3) ' x 5,x 0,x 2 x(x + 5) lgebra II Rationals Post-Test Page 11

12 33 Write the equation of the parent function f(x) = 1, after a translation of 3 to the left and 5 down. x f(x) = 1 x C f(x) = 1 x 3 5 f(x) = 1 x D f(x) = 1 x The graph below is a transformation of the parent function f(x) = 1. Write the equation of the graph. x f(x) = C f(x) = x 1 x 1 5 f(x) = D f(x) = x + 1 x lgebra II Rationals Post-Test Page 12