Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Answers for the lesson “Graph Square Root and Cube Root Functions” LESSON 3.5 Skill Practice y 6. 1. radical 2 21 x 2. a. The graph will be reflected over the x-axis and will rise faster. b. The graph will be translated 2 units right. c. The graph will be translated domain: xq0, range: ya0 4 units up. 1 21 y 7. y 3. x Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 2 21 domain: xq0, range: ya0 4. f(x) x domain: xq0, range: yq0 g(x) 8. 1 21 x domain: xq0, range: f(x) q0 5. 21 y 1 21 3 x domain: xq0, range: g(x)q0 x 9. D domain: xq0, range: ya0 Algebra 2 Answer Transparencies for Checking Homework 104 10. y 13. y 1 4 0.2 22 x 22 x domain: all real numbers, range: all real numbers y 11. domain: all real numbers, range: all real numbers 1 y 14. 22 x 3 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 22 x domain: all real numbers, range: all real numbers y 12. domain: all real numbers, range: all real numbers 2 22 15. y x 1 22 domain: all real numbers, range: all real numbers x domain: all real numbers, range: all real numbers Algebra 2 Answer Transparencies for Checking Homework 105 16. y 19. y 1 22 x domain: all real numbers, range: all real numbers 1 21 x y 20. domain: xq1, range: yq3 y 17. 1 2 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 21 22 x domain: all real numbers, range: all real numbers domain: xq21, range: yq8 y 18. domain: xq5, range: ya1 y 21. 1 21 x x 2 22 x domain: all real numbers, range: all real numbers Algebra 2 Answer Transparencies for Checking Homework 106 22. 25. The domain is limited because the y 2 22 x square root of a negative number is not a real number. The range is limited because the square root of a number is nonnegative. 26. The graph was translated domain: xq4, range: ya27 23. y 1 22 x horizontally in the wrong direction; the graph of 3} y 5 22Ïx 1 1 2 3 is the 3} graph of y 5 22Ï x translated left 1 unit and down 3 units. 27. C Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 28. Domain: xq25, range yq0; the expression under the radical sign must be greater than or equal to 0, so substitute the least value of x into the equation and find y. domain: all real numbers, range: all real numbers 24. y 29. Domain: xq12, range: yq0; the expression under the radical sign must be greater than or equal to 0, so substitute the least value of x into the equation and find y. 30. Domain: xq0, range: yq24; the 2 21 x domain: all real numbers, range: all real numbers expression under the radical sign must be greater than or equal to 0, so substitute the least value of x into the equation and find y. 31. Domain: all real numbers, range: all real numbers; there are no restrictions on finding the cube root of a number and therefore no restrictions on the range. Algebra 2 Answer Transparencies for Checking Homework 107 Î } 32. Domain: all real numbers, range: all real numbers; there are no restrictions on finding the cube root of a number and therefore no restrictions on the range. 165 39. a. vt 5 33.7 } A b. Sample: A vt 306.1 33. Domain: xq3, range: yq6; the expression under the radical sign must be greater than or equal to 0, so substitute the least value of x into the equation and find y. 34. Sample answer: If n is even, the graph will have a restricted domain and range. If n is odd, the domain and range will be all real numbers. 2 A 8 4 6 216.44 176.72 10 vt 153.05 136.89 c. Vt 500 400 300 200 35. about 43 ft above sea level 36. a. about 1.6 sec b. about 3.25 ft Î } C 37. a. v 5 331.5 1 1 } 273.15 b. domain: Cq2273.15, range: vq0 38. about 2470 horsepower Speed (mi/h) Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Problem Solving s 250 200 150 100 50 0 0 1000 2000 3000 p Power (horsepower) 100 0 0 2 4 6 8 10 A S 40. a. S 5 :r 2 1 :r, }F 5 r 2 1 r, : 1 1 S 4 4 : 1 1 2 S }5 r1} , }F 1 4 2 : } 1 1 S } 5 r 1 }, }F 1 4 2 : } 1 4S 1 : } F 5 r 1 }, 2 4: } 1 : 1 } } S 1 } 5 r 1 }, 2 4 Ï :F } 1 : 1 } } S 1 } 2 } 5 r 2 4 Ï :F }F 1 } 5 r 2 1 r 1 }, Î Î 1 2 Î Î Algebra 2 Answer Transparencies for Checking Homework 108 40. b. r 2 1.5 1 0.5 0 2 4 6 8 S Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 0 Algebra 2 Answer Transparencies for Checking Homework 109