With Great Power... Inverses of Power Functions. Lesson 9.1 Assignment. 1. Consider the power function, f(x) 5 x 7. a. Complete the table for f(x).
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1 Lesson.1 Assignment Name Date With Great Power... Inverses of Power Functions 1. Consider the power function, f(x) 5 x 7. a. Complete the table for f(x). x f(x) b. Sketch the graph of f(x) y x c. Is f(x) invertible? Explain your reasoning. Chapter Assignments 125
2 Lesson.1 Assignment page 2 d. If f(x) is invertible, sketch the graph of f 21 (x). 4 y x Consider the power function, g(x) 5 x 8. a. Complete the table for g(x). x g(x) b. Sketch the graph of g(x) y x c. Is g(x) invertible? Explain your reasoning. 126 Chapter Assignments
3 Lesson.2 Assignment Name Date The Root of the Matter Radical Functions 1. Brian has a new beehive. The number of bees in the hive after x weeks can be modeled by the function b(x) 5 36x 2 for 1 # x # 30. a. Determine the corresponding range of b(x) for the given domain. Describe what the domain and range represent in this problem. b. Graph the function b(x) with the given domain restrictions. y Bee Population (thousands) x Time Since Brian Got New Beehive (weeks) c. Use the function b(x) to predict the bee population after 10 weeks. d. Use the function b(x) to predict the bee population after 20 weeks. Chapter Assignments 127
4 Lesson.2 Assignment page 2 e. Write the inverse function b 21 (x). f. Use compositions to verify that b(x) and b 21 (x) are inverse functions. Show your work. g. Determine the domain and range of b 21 (x). Describe what the domain and range represent in this problem. 128 Chapter Assignments
5 Lesson.2 Assignment page 3 Name Date h. Graph the inverse function b 21 (x). Label and number each axis accordingly. y x i. Use the inverse function to determine when the bee population will be 25,000. Chapter Assignments 12
6 130 Chapter Assignments
7 Lesson.3 Assignment Name Date Making Waves Transformations of Radical Functions 1. Brandon, a graphic designer, designed the logo shown for the Lazy Y Ranch. Each curve in the design is a transformation of the cube root function f(x) 5 3 x with a restricted domain. 8 y 6 4 n(x) 2 m(x) g(x) x 24 h(x) a. Describe each of the four transformations of f(x) 5 3 x that were used to create the four functions in the design. b. Write each function used in the design. For each function, write the domain as an inequality. Chapter Assignments 131
8 Lesson.3 Assignment page 2 2. Brandon is working on a logo for a publishing company. He starts by graphing the function r(x) 5 x with the restricted domain 0 # x # 6. He plans to add the graphs of 5 more functions to complete the design. y r(x) x a. The next function Brandon adds is s(x), which is the square root function after a vertical stretch by a factor of 2 and a translation 1 unit up. Write the function s(x) and graph s(x) with the domain 0 # x # 6. b. Next, Brandon adds the function t(x), which is the square root function after a vertical stretch by a factor of 3 and a translation 2 units up. Write the function t(x) and graph t(x) with the domain 0 # x # 6. c. To complete the design, Brandon adds the functions r(x), s(x), and t(x) which are reflections of the original 3 functions across the y-axis. Write the functions r(x), s(x), and t(x) and graph each function with the domain 26 # x # Chapter Assignments
9 Lesson.4 Assignment Name Date Keepin It Real Extracting Roots and Rewriting Radicals 1. Luke was asked to rewrite the radical a 5 b 2 after extracting all possible roots. His work is shown. a 5 b 2 5? a 5? b 2 5? a 4? a? b a 2 b a a. Identify the error(s) in Luke s work. b. Correctly rewrite the radical a 5 b 2 after extracting all possible roots. 2. Elena was asked to rewrite the radical 3 24 x 3 y 6 after extracting all possible roots. Her work is shown x 3 y ? 3 x 3? 3 y ? 3 3? x? y 2 5 2? 1? x? y x y 2 a. Identify the error(s) in Elena s work. b. Correctly rewrite the radical 3 24 x 3 y 6 after extracting all possible roots. Chapter Assignments 133
10 Lesson.4 Assignment page 2 3. Rewrite 50 a 3 b 4 in exponential form. Then, rewrite the expression in radical form after extracting all possible roots. 4. Rewrite 3 27m 8 n 6 t 4 in exponential form. Then, rewrite the expression in radical form after extracting all possible roots. 5. Rewrite 4 48 x 5 y 16 in radical form after extracting all possible roots. 6. Rewrite (x 2 5) 2 in radical form after extracting all possible roots. 7. Rewrite (8 1 m) 4 in radical form after extracting all possible roots. 134 Chapter Assignments
11 Lesson.5 Assignment Name Date Time to Operate! Multiplying, Dividing, Adding, and Subtracting Radicals 1. Leland multiplied 4 3 x 2? 5 x 3, given x $ 0. His work is shown. 4 3 x 2? 5 x 3 5 4x 2 3? 5x x x a. Identify the error(s) in Leland s work. b. Correctly multiply 4 3 x 2? 5 x 3, given x $ 0. Write your answer in radical form. 2. Kata combined the like terms in the problem 12 3 m m m 2. Her work is shown m m m 2 5 m 2 3 m 2 5 m 3 m 2 a. Identify the error(s) in Kata s work. b. Simplify 12 3 m m m 2. Write your answer in radical form. Chapter Assignments 135
12 Lesson.5 Assignment page 2 3. Divide 4 3 x 2 3, given x. 0. Extract all roots and write your answer in radical form without radicals in 16x the denominator. 4. Simplify 6 3 x 2 (15 3 x x ) 1 8x. Write your answer in radical form. 5. Simplify 24.1 m ( m 2 6 n ) n (4 m 2 7 n ), given m $ 0 and n $ 0. Write your answer in radical form. 6. Fill in the empty box with the radical expression that correctly satisfies the equation. 2 3 x x 7. Fill in the empty box with the radical expression that correctly satisfies the equation.? (3 x 2 2 y ) 5 18 x 212 xy 136 Chapter Assignments
13 Lesson.6 Assignment Name Date Look to the Horizon Solving Radical Equations 1. The perimeter of the given rectangle is 20 inches. Determine the value of x and check your solution. x!x The length, d, of the diagonal in a right rectangular prism can be determined using the equation d 5 l 2 1 w 2 1 h 2, where l represents the length, w represents the width, and h represents the height. Determine the height of a right rectangular prism with a length of 8 inches, a width of 4 inches, and a diagonal length of 12 inches. Check your solution. d h l w Chapter Assignments 137
14 Lesson.6 Assignment page 2 3. Jackson solved the radical equation 3 2x His work is shown. 3 2x ( 3 2x 2 5 ) 3 5 (5) 3 2 x x x x x 5 5 a. Identify the error(s) in Jackson s work. b. Correctly solve 3 2x Check your solution. 4. Solve x 1 x and check your solution. 5. Solve.7x and check your solution. 138 Chapter Assignments
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