Answers to Algebra 2 Unit 5 Practice

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1 Lesson -. D. C. a. domain: [6, `), range: [0, `) Answers to Algebra Unit 5 Practice b. domain: [0.5, `), range: (`, ] c. domain: [0, `), range : [, `) 4. If the variable under the radical is, adding to or subtracting from shifts the position of the graph left or right along the -ais. Because the domain of the function under the square root radical must alwas be equal to or greater than zero, the domain shifts along the -ais as well. 5. a. f () (4., 5). a b. no real roots c. 5.5 b. At least units of fuel are needed to get the ship to start moving. The graph indicates that the speed does not rise above 0 until.. Lesson -. A. g () is a compression of f () b a factor of.. f () 5 4. The domain and range for this function are all real numbers. Lesson - 6. B 7. B units 5 College Board. All rights reserved A

2 5. The product of a real number multiplied b itself can never be less than zero. The product of a real number multiplied b itself twice will be a negative number if the original real number is negative. 0. domain:. 0, range: $ f () Lesson B 7. 5 f() 8. 9 units 9. (.75,.8). a. 5 0 b. 5 c. 5 6 Lesson 6-. D. C. Answers will var, but should include either an algebraic solution such as f () 5, f () 5, and f () 5, or a graph of the function and its inverse showing the point of intersection. 4. The domain of f is the same as the range of f, and the range of f is the same as the domain of f.. a. es b Substitute the given input values for into the given function and compare them to the given output values. As the values are similar, the model appears to be appropriate. Lesson 6-. Stace is incorrect. A one-to-one function must also pass the horizontal line test. This function does not pass it, so it is not one-to-one.. The function is one-to-one. The graph passes the horizontal line test.. D 4. A 5. Yes; since the function is simpl a translation of the parent function, it is also one-to-one. Lesson p() 5, # # Lesson 6-6. C 7. domain: $ 4, range: $ 0 8. es, $ or # 9. No, there is no effect, as the constants onl translate the original function verticall and/or horizontall students minimum s() 5, # # , 5.99 There need to be at least students. 5 College Board. All rights reserved A

3 40. 0 p() s() 0 The second function ehibits a greater reduction in per-student pricing because the domain is much less restricted. Lesson 7-4. {b: 0, b # }; at bear populations of less than, the calculated deer population approaches infinit. At bear populations of greater than, there is a negative number of deer {: 5, # 0} 49. {: 0 # }; (0, `). Answers will var. One possibilit is that there are 5 apples located in places inaccessible to the birds, regardless of the number of birds in the area. Lesson k z 5. a. F g 5 gmm r b. N 54. D 55. It is false because the inverse variation indicates that changes b a factor of deer 44. The function would be increased b s: 7b P(b) 5 s. b 45. The reasonable domain would etend indefinitel past. Lesson There are 0 undamaged apples. Using the function N(b), N(0) 5 0; using the graph, the -intercept is about 0. Lesson D 57. f () intercept:., -intercept: 4.5, vertical asmptote: 5, horizontal asmptote: Sadra is incorrect. Eplanations ma var but should include a countereample such as or other solid reasoning units of pressure Lesson 9-6. B 6. D 4 6., fi,,, No; Claire did not correctl cancel ( 4) in the numerator and denominator. The correctl simplified function is and the domain restriction is fi 4,. 5 College Board. All rights reserved A 65. 5, 5,

4 Lesson 9- Lesson ,, A 77. a. 67.,, 68. A and C 69. LCD: (5 ); ( 9) (5 ), 0, a. Yes, ( 5) ( ) 5 and ( ) 5 5. b. fi Lesson 9-7. B 7. D 7. horizontal asmptote at 5 0, vertical asmptote at 5 5, hole at vertical asmptote at 5 4, holes at 5 0 and 5 b. vertical asmptotes at 5 4 and 5, horizontal asmptote at 5 0, no holes 78. domain: { [ : fi and fi 4} a. 5 b c. no horizontal asmptote d. 5 5 vertical asmptotes at 5 and 5, horizontal asmptote at He was incorrect, as there is a hole at 5 but no asmptote at 5. His error was likel the result of incorrectl interpreting the cancellation of ( ) in the numerator and denominator after factoring. 5 College Board. All rights reserved A4

5 Lesson C It is reasonable. Eplanations will var but might include: tons of cargo ever 5 minutes equals 0 tons of cargo ever hour. So if both cranes together can unload 0 tons of cargo in an hour, it is reasonable to assume that each crane could unload 0 tons of cargo during that hour. Lesson B 87.,,.5 or. 0 0,000, C() ,000,000 or more 90.,, 0 or. 85. B: 4 milliseconds, A: milliseconds 5 College Board. All rights reserved A5