Drill 2-1 - to(aqt73 – Drill 2 – seckin –(54330 This...

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Unformatted text preview: to (aqt73) – Drill 2 – seckin – (54330) This print-out should have 28 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 4) 10.0 points f ( x) = 2 x − 5 , g ( x) = 1 − x. Find a) (f + g )(x). 1. 3x − 6 2. x − 6 3. None of these 4. −3x + 6 5. x − 4 002 (part 2 of 4) 10.0 points b) (f − g )(x). 1. None of these 1 004 (part 4 of 4) 10.0 points f g d) (x) and its domain. 1. None of these 2x − 5 , x−1 2x − 5 3. , 1−x 1−x 4. , 2x − 5 x−1 , 5. 2x − 5 2. x=1 x=1 5 2 5 x= 2 x= 005 10.0 points Simplify as much as possible the expression for the function h = 2f − g when f ( x) = x 2 − 3 x + 3 , g ( x) = x 2 − 2 x − 2 . 2. x − 6 1. h(x) = x2 − 4x + 8 3. 3x − 6 2. h(x) = 3x2 − 8x + 4 4. x − 4 3. h(x) = x2 − 4x + 4 5. −3x + 6 4. h(x) = 3x2 − 4x + 4 003 (part 3 of 4) 10.0 points c) (f g )(x). 1. 3x − 6 2 2. 2x + 3x − 5 3. −2x2 − 3x + 5 4. x − 4 5. h(x) = 3x2 − 8x + 8 6. h(x) = x2 − 8x + 8 006 (part 1 of 2) 10.0 points When f and g are given by 4 3 2 5. 2x + 7x + 5 6. None of these 7. −2x2 + 7x − 5 f ( x) 2 1 1 2 3 4 to (aqt73) – Drill 2 – seckin – (54330) 2 4 2. F (x) = x2 + 3x + 10 3 3. F (x) = x2 + 7x + 10 g ( x) 2 4. F (x) = x3 − 6x2 + 3x + 4 1 5. F (x) = x3 + 3x + 8 1 2 3 4 6. F (x) = x2 + 7x + 8 (i) determine the value of (f − g )(0). 007 (part 2 of 2) 10.0 points (i) Determine the value of (f g )(3). 012 10.0 points Find the composition f ◦ g of the functions f ( x) = x−3 , x2 g ( x) = 3 x + 1 . 008 (part 1 of 3) 10.0 points The graph of two functions is shown in x−3 + 6x + 1 1. (f ◦ g )(x) = 9 x2 4 2. (f ◦ g )(x) = 3 x2 − 8 x − 3 x2 2 3. (f ◦ g )(x) = 9 x2 4. (f ◦ g )(x) = x2 − 6 x + 9 x2 5. (f ◦ g )(x) = 3x − 2 x2 6 y 5 4 3 2 3x − 2 + 6x + 1 1 x 0 -1 -2 -3 −2 2 −2 f: g: -4 -3 -2 -1 0 4 1 2 3 4 1. What is the value of (f + g )(4)? 009 (part 2 of 3) 10.0 points 2. What is the value of (f · g )(2)? 010 (part 3 of 3) 10.0 points f (3)? 3. What is the value of g 011 10.0 points What is the composition, F = f ◦ g , of f ( x) = x 2 + 5 x + 4 , g ( x) = x + 1 . 1. F (x) = x3 + 6x2 + 9x + 4 013 5 10.0 points Determine the value of (g ◦ f )(1) when f ( x) = x+2 , x 1. (g ◦ f )(1) = 4 2. (g ◦ f )(1) = 5 3. (g ◦ f )(1) = 6 4. (g ◦ f )(1) = 3 g ( x) = x 2 − 4 . to (aqt73) – Drill 2 – seckin – (54330) 5. (g ◦ f )(1) = 7 014 (part 1 of 3) 10.0 points √ f ( x) = 3 x − 1 , g ( x) = x 3 + 1 Find f ◦ g . 3 7. x 017 (part 1 of 2) 10.0 points f (x) = x2/3 , g ( x) = x 6 Find f ◦ g . 2 1. x3 + 1 1. x 3 2. None of these 2. x4 3. 3 x3 + 1 3. x6 4. x 4. x9 5. x + 1 5. None of these 6. x3 015 (part 2 of 3) 10.0 points Find g ◦ f . 018 (part 2 of 2) 10.0 points Find g ◦ f . 1. x6 2 1. None of these 2. x 3 2. x3 + 1 3. x9 3. x 4. x4 4. x3 5. None of these 5. x + 1 6. 3 x3 + 1 016 (part 3 of 3) 10.0 points Find f ◦ f . √ 1. 3 x 2. 3. √ 9 3 019 (part 1 of 2) 10.0 points Match the function f ( x) = | x − 6 | + 7 with its graph. 1. None of these 12 x−1−1 √ 3 x−1−1 √ 4. 9 x − 1 √ 5. 9 x − 1 6. None of these 2. 10 8 6 4 2 −2 2 to (aqt73) – Drill 2 – seckin – (54330) 12 10 12 10 3. 4 1. 8 6 4 2 8 6 4 2 −2 2 46 −2 8 10 12 24 6 8 10 12 24 6 8 10 12 2 12 2. 10 8 4. −6 −8 6 4 2 −12 10−8 −6 −4 −2 − −2 −2 −4 3. None of these 2 2 2 5. 4. −2 −2 −4 −6 2 46 −12 10−8 −6 −4 −2 − −2 2 −4 −6 −8 8 10 12 −8 2 020 (part 2 of 2) 10.0 points Match the function b) 5. −2 −2 −4 24 6 8 10 12 −6 −8 f ( x) = | x + 7 | − 3 with its graph. 021 10.0 points Find the function g that results after the following transformations are applied in the order given to the graph of a function f : (1) stretch along y -axis by a factor 8; (2) reflect about the x-axis; to (aqt73) – Drill 2 seckin – (54330) (3) shift down 3 units; (4) reflect about the y -axis. 1. g (x) = 24 − 3f (−x) 2. g (x) = 24 + 8f (−x) 3. g (x) = −3 − 8f (−x) 4. g (x) = 8f (x) − 24 5 4.4 2 3 1 2 −1 −1 1 0 1 2 3 −2 -1 5 -3 -2 -1 0 1 2 5.4 1 3 5. g (x) = 24 − 8f (x) 022 5 1 2 10.0 points Which of the following is the graph of y = 2 − f (x − 1) −1 2 3 4 1 −2 0 −3 -1 5 -3 -2 -1 0 1 2 2 when f (x) = x ? 6.4 5 3 3 1.4 3 1 −1 −1 0 -1 5 -3 1 2 3 −4 −3 −2 −1 −1 0 -1 −2 -2 1 1 2 1 2 2 2 -3 -1 2.4 0 1 2 -2 -1 0 g ( x) = 1 2 −3 −2 −1 −1 1 0 -1 5 -3 1 −2 -2 -1 3.4 0 1 2 2 3 1 2 −3 −2 −1 −1 1 0 1 −2 -1 -3 -2 -1 0 2 023 10.0 points Explain how the graph of 2 3 1 √ x−2+9 can be obtained from the graph of f (x) = 2 x. 1. A shift to the right by 2 and a shift up by 9. √ 2. A shift to the right by 2 and a shift up by 9. √ 3. A shift to the left by 2 and a shift down bt 9. 4. Shift up by 2. 5. A stretch by 2 and a shift up by 9. 1 √ to (aqt73) – Drill 2 – seckin – (54330) 6. A shift to the left by 2 and a shift down by 9. √ 7. A stretch by 2 and a shift down by 9. 6 6 4 4. 2 −4 −2 8. None of these 2 4 9. Shift down by 2. 024 10.0 points Sketch the graph of the function. 5. None of these 4 2 6. f (x) = −|x| − 6 . −10 −8 −6 −4 −2 −4 −2 2 4 025 (part 1 of 4) 10.0 points Consider the graph of y = f (x). −2 7 −4 1. 6 6 5 4 4 −6 3 2 2 −8 1 0 −10 −4 −2 -1 -2 -6 -5 -4 -3 -2 2 -1 0 1 4 2 3 4 5 7 6 6 2. 2 4 6 8 −2 10 5 1. 4 4 3 −4 2 2 1 0 10 −4 −2 −2 -1 -2 8 -3 6 -5 -6 4 -7 -6 -5 -4 -3 -2 −6 -1 2 2. None of these −4 −2 2 4 2 4 −4 -4 3. 6 What is the graph of y = f (x + 3)? 0 1 2 3 4 5 6 to (aqt73) – Drill 2 – seckin – (54330) 10 3. 10 9 7 9 8 8 4. 7 8 8 7 6 6 6 6 5 5 4 4 4 4 3 3 2 2 2 2 1 1 0 0 −4 −2 -1 -2 -6 -5 -4 -3 2 4 −4 −2 -1 -2 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 2 -1 0 1 2 4 3 4 5 6 5 6 7 6 6 4. 5 4 4 3 2 2 7 6 6 1 5 5. 0 −2 -1 -2 -3 -2 2 4 6 4 4 3 -1 0 1 2 3 4 5 6 7 2 7 2 6 6 5. 1 5 0 4 4 −4 −2 −2 -1 3 -2 2 2 -3 -4 0 -5 −8 −6 −4 −2 -2 -6 -7 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 4 −4 1 -1 2 2 -6 -5 -4 -3 -2 −6 -1 0 1 2 3 4 026 (part 2 of 4) 10.0 points What is the graph of y = f (x) + 3? 7 6 6 1. 027 (part 3 of 4) 10.0 points What is the graph of y = 2f (x). 5 4 4 3 2 2 10 9 1 1. 0 −2 -1 -2 -3 -2 2 4 6 8 8 7 6 6 -1 0 1 2 3 4 5 6 7 7 5 6 6 2. 4 4 5 3 4 4 2 2 3 1 2 2 0 −4 −2 1 -1 0 -2 -6 −8 −6 −4 −2 -1 -2 -9 -8 -7 -6 -5 -4 3. None of these -3 -2 -1 0 1 2 -5 -4 -3 -2 2 -1 0 1 2 4 3 4 5 6 to (aqt73) – Drill 2 – seckin – (54330) 1 What is the graph of y = − f (x) + 3? 2 15 14 14 8 13 5 2. 12 12 4 4 11 3 10 10 8 8 2 2 1. 9 1 0 −4 −2 −2 7 -1 6 6 -2 5 -3 4 4 -5 2 4 −4 -4 3 2 2 −6 -6 1 -7 0 −4 −2 -1 -2 -6 -5 -4 -3 -2 2 4 −8 -8 -9 -1 0 1 2 3 4 5 6 −10 -10 2 -11 1 −12 -12 0 3. −4 −2 −2 -1 -2 -3 2 4 -13 -14 -15 -6 −4 -4 -5 -7 -9 -11 -13 -14 -15 -6 -5 -4 -3 −14 -2 -1 -2 -1 0 1 2 3 4 5 6 5 6 5 6 4 2 2 2. 1 0 −4 −2 −2 -1 -2 −12 -12 −14 3 −10 -10 -3 4 −8 -8 -4 5 −6 -6 -5 -3 -5 −6 -6 1 2 3 4 5 6 -7 4. None of these 4 −4 -4 0 2 −8 -8 -9 15 14 14 −10 -10 -11 13 5. 12 12 −12 -12 -13 11 10 10 -14 -15 -6 -5 -4 -3 −14 -2 -1 0 1 2 3 4 9 8 8 5 4 7 4 3. 6 6 3 2 5 2 4 4 1 3 0 2 2 −4 −2 −2 -1 1 -2 0 -3 −4 −2 -1 -2 2 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 4 -4 -5 -6 2 6 -6 -6 028 (part 4 of 4) 10.0 points -5 -4 -3 -2 -1 0 1 2 3 4 to (aqt73) – Drill 2 – seckin – (54330) 2 4. 1 0 −4 −2 −2 -1 -2 -3 2 4 −4 -4 -5 -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 5 6 5 4 4 5. 3 2 2 1 0 −4 −2 −2 -1 -2 -3 2 4 −4 -4 -5 -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 9 ...
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This note was uploaded on 06/14/2011 for the course MATH 305G taught by Professor Cathy during the Spring '11 term at University of Texas.

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