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

Transcription

1 Name: _ Class: _ Date: Rationals Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Solve the equation for g: 3 2g + 1 6g = C D Given the graph of the function f(x) = 1. Which of the following represents the behavior of the function as x x approaches negative infinity? approaches negative infinity C approaches positive infinity approaches one D approaches zero

2 (x 3)(x + 1)(x 7) 3 State the domain of the function y =. (x + 8)(x + 2) Ï Ô Ï Ìx x 8,x 2} ÓÔ C Ô Ìx x 3,x 1,x 7} ÓÔ Ï Ô x Ï Ì x 8,x ÓÔ 2} D Ô Ìx x R} ÓÔ 4 Simplify: 4 c c c 2 + c 90 8 (c 9)(c + 9) C D 4c 32 (c 9)(c + 9) 4c + 40 (c 9)(c + 9) lgebra II Rationals Pre-Test Page 2

3 5 Sketch the asymptotes and graph the function. y = x 2 + 2x 3 x 2 25 C D 6 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 25 ohms and r 2 is 95 ohms. Round your r 1 r 2 answer to the nearest ohm if necessary. 34 ohms C 129 ohms 2255 ohms D 20 ohms lgebra II Rationals Pre-Test Page 3

4 7 Describe the vertical asymptote(s) and hole(s) for the graph of y = (x + 1)(x + 4) (x + 4)(x 5). asymptotes: x = 5 and x = 4 C asymptote: x = 5 and hole: x = 4 asymptote: x = 5 and hole: x = 4 D asymptote: x = 1 and hole: x = 5 8 Simplify the expression and state the excluded values: g 2 + 7g 8. g + 8 g + 1; g 8 C g 1; g 8 g + 1; g 8 D g 1; g 8 9 Which family of functions does y = 1 belong to? 2 x Trigonometric C Exponential Logarithmic D Rational lgebra II Rationals Pre-Test Page 4

5 10 Solve the equation for x: 1 x + 3 = 5 x C D Which of the following functions is not rational? f(x) = 1 x 2 C (x) = f(x) = x 8 x + 16 D f(x) = x 2 1 x 2 + 2x + 1 5x x 2 12 Determine the horizontal asymptotes of the function: g(x) = x x 3. Horizontal asymptote: y = 4 C Horizontal asymptote: y = 3 There is no horizontal asymptote D Horizontal asymptote: y = 3 13 Describe the holes for the graph of the the rational function y = (x 8) (x 8)(x + 9). Hole: x = 8 C Hole: x = 8 Hole: x = 9 D Hole: x = 9 lgebra II Rationals Pre-Test Page 5

6 14 Which function does not have a horizontal asymptote. g(x) = x 3 3 6x 2 7 g(x) = x 2 5x C g(x) = x 8 x + 3 D g(x) = x 6 x Determine the end behavior of the function. f(x) = (x 3) (x 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. lgebra II Rationals Pre-Test Page 6

7 16 Reduce the fraction to lowest terms: 18x 2 + 6x. 6x 3x + 1 C 2x x D 6x Solve the equation 1 x x 3 = 9 for x. x 2 9 x = 3 C No solution x = 9 D x = 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 8 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 + 8 x = 1; 15 hours C x 8 + x 7 = 1; 7.5 hours = 1 x ; 7.5 hours D x 7 + x 8 = 1; 3.7 hours 19 Determine the horizontal asymptote of the function. y = x x 2 3. y = 1 C y = 4 3 y = 3 4 D y = 4 3 lgebra II Rationals Pre-Test Page 7

8 20 Simplify the following expression: y 3 y + 3 y + 5 y 2 + 4y + 3. (y 3)(y + 5) (y + 3) 2 (y + 1) (y 3)(y + 1), y 3, 1 C ;y 3, 1, 5 y + 5 (y 3)(y + 1), y 1, 5 D y + 5 (y 3)(y + 5), y 3, 1, 5 (y + 3) 2 (y + 1) 21 Solve for y, then graph the function. xy + 18 = 0 C D lgebra II Rationals Pre-Test Page 8

9 22 Find the x intercepts of the function: h(x) = x 2 3x + 2. x 2 4 (0,1) C (1,0) (0, 1) D ( 1,0) 23 Describe the vertical asymptote(s) and hole(s) for the graph of y = (x + 3)(x 6) (x 1)(x + 3). asymptote: x = 6 and hole: x = 3 C asymptote: x = - 6 and hole: x = 3 asymptote: x = 6 and hole: x = 3 D asymptote: x = 1 and hole: x = Which equation best represents the graph? (x 3) y = (x 6) (x + 3) y = (x + 6) (x + 6) C y = (x 3) (x + 3) D y = (x 6) lgebra II Rationals Pre-Test Page 9

10 25 What are the x and y-intercepts of the rational function R(x) = x 2 2x 1? x + 1 x-intercepts: none y-intercept: (0, 1) C x-intercepts: (1 ± 2, 0) y-intercept: (0, 1) x-intercepts: (1, 0) and (2, 0) y-intercept: (1/2, 0) D x-intercepts: (-1, 0) and (-2, 0) y-intercept: ( 1, 0) 26 Find any points of discontinuty for the rational function: y = (x + 2)(x + 3)(x + 9). (x 8)(x 5) x =2, x =3, x = 9 C x = -8, x = -5 x = 5, x = 8 D. x = -2, x = -3, x = What are the vertical and horizontal asymptotes of the rational function? 1 y = x Vertical ysmptotes: x = 4 Horizontal symptotes y = 5 Vertical ysmptotes: x = 5 Horizontal symptotes y = 4 C Vertical ysmptotes: x = 5 Horizontal symptotes y = 4 D Vertical ysmptotes: x = 5 Horizontal symptotes y = -4 lgebra II Rationals Pre-Test Page 10

11 28 Multiply. State the excluded values. d 2 d + 1 d 2 + 4d + 3 d 2 + 6d d 2 + 3d d + 3, d 1, 0, 6 C, d 1, 0, 6 d + 6 d + 6 d 2 + 3d d + 6, d 1, 6 D d + 3 d + 6, d 1, 6 29 Simplify the following rational expression, state any excluded values. 5x x 2 x 6 4 x 2 + 4x + 4 5x 2 + 6x + 12 (x 3)(x + 2),x 3,x 2 C 5x 2 + 6x 12,x 3,x (x 3)(x + 2) 5x x + 12 (x 3)(x + 2),x 3,x 2 D 5x x 12,x 3,x (x 3)(x + 2) 30 Simplify the following rational expression, state any excluded values. 2x x x 2 2x 2 (x 2 1),x 0,x ±1 C 2x 3 x 2 + 1,x 0,x ±1 x 2 (x 2 1) 2x 3 + x 2 1 x 2 (x 2 1),x 0,x ±1 D 2x 3 + x 2 + 1,x 0,x ±1 x 2 (x 2 1) lgebra II Rationals Pre-Test Page 11

12 31 Simplify the following rational expression, state any excluded values.. 8x 2 4x 10x 5 5x 15 3x x 3 C 4(x 2),x 0.5,x 3 3(x 3) 4x, x 0.5,x 3 D, no restrictions 3 32 Simplify the following rational expression, state any excluded values.. x 2 x 2 + 2x + 1 3x x 2 1 x 3 3x 3 (x 2 1)(x 2 + 2x + 1) 2 x(x 1) ' x ±1,x 0 C 3(x + 1) ' x ±1,x 0 ' x ±1,x 0 D x(x 1) 3(x + 1) ' x ±1,x 0 33 Write the equation of the parent function f(x) = 1, after a translation of 2 to the right and 4 down. x f(x) = 1 x 2 4 C f(x) = 1 x f(x) = 1 x D f(x) = 1 x lgebra II Rationals Pre-Test Page 12

13 34 The graph below is a translation of the parent function f(x) = 1. Write the equation of the graph. x f(x) = 1 x C f(x) = 1 x f(x) = 1 x 4 3 D f(x) = 1 x lgebra II Rationals Pre-Test Page 13