University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2019
Views:

470

Pages:

3
Author:

lankstoetp11

Algebra 2 Chapter 7 Review Name: Key Date: 7.1 In Exercises 1-6, tell whether x and y show direct variation, inverse variation, or neither. 1. x = 7/y Inverse 2. y = 6x Direct 3. x + y = 8 Neither In Exercises 4-10, tell whether x and y show direct variation, inverse variation, or neither. 4. x | 2 | 4 | 8 | 10 y | 38 | 19 | 9.5 | 7.6 Direct 5. x | 3 | 5 | 8 | 10 y | 15 | 9 | 6 | 5.5 Neither 6. x | 1.5 | 4.5 | 6.5 | 10 y | 9 | 24 | 39 | 60 Direct In Exercises 7-13, the variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 3. 7. x = 6, y = -5 a = 6(-5) a = -30 y = -30/x x = 3, y = -10 8. x = 3, y = 2/3 a = 3 * 2/3 = 2 y = 2/x x = 3, y = 2/3 9. The number y of songs that can be stored on an MP3 player varies inversely with the average size x of a song. A certain MP3 player can store 3000 songs when the average size of a song is 5 megabytes. Find the number of songs that will fit on the MP3 player when the average size of a song is 4 megabytes. y = a/x a = 3000(5) a = 15000 y = 15000/x y = 3750 songs will fit if the average size is 4 megabytes. 7.2 In Exercises 4-15, graph the function. State the domain, range, vertical and horizontal asymptote. 10. g(x) = 3/(x+4) VA: x = -4 D: R, x ≠ -4 HA: y = 0 R: R, y ≠ 0 11. y = -2/(x+1) + 3 VA: x = -1 D: R, x ≠ -1 HA: y = 3 R: R, y ≠ 3 12. g(x) = (x-3)/(2x+8) VA: x = -4 D: R, x ≠ -4 HA: y = 1/2 R: R, y ≠ 1/2 7.3 In Exercises 1-6, simplify the expression, if possible. 13. 4x^2 / 4x^2 = 1 14. (x^2 + 5x + 6) / (x^2 + 2x - 3) = (x+3)(x+2) / (x+3)(x-1) = (x+2)/(x-1) 15. (5x^2 - 3x^2 + 20x - 12) / (x^4 - 16) = (2x^2 + 20x - 12) / (x^2 + 4)(x^2 - 4) = (2(x+6)(x-1)) / ((x^2 + 4)(x+2)(x-2)) In Exercises 7-12, find the product. 16. (x-4)(x+3) = x^2 - x - 12 17. (x-2)(x+1) / 3x * 3x(x+7) / (x-4)(x-2) = (x+1)(x+7) / (x-4) 18. (x^2 + 8x + 16) / (x^2 - 2x - 3) * (x^2 - 9) / (x^2 + 5x + 4) = (x+4)(x+4)(x+3)(x-3) / (x+4)(x-3)(x+1)(x+4) = (x+3)/(x+1) 19. (x^2 + 3x - 28) / (x^2 - 25) * (x^2 - 8x + 15) = (x+7)(x-4)(x-3)(x-5) / (x+5)(x-5) = (x+7)(x-4)(x-3) / (x+5) In Exercises 13-21, find the quotient. 20. (x^2 - 2x - 3) / (x^2 + 2x - 8) + (x^2 + 4x + 3) / (x^2 + 6x + 8) = (x-3)(x+1) / (x+4)(x-2) + (x+3)(x+1) / (x+4)(x+2) = (x-3)(x+1)(x+2) + (x+3)(x+1)(x-2) / (x+4)(x-2)(x+2) = (x-3)(x+1) / (x+4)(x-2) In Exercises 22-23, find the sum or difference. 22. (2x^2 + 8x) / (x+6) = 2x(x+4) / (x+6) 23. (3x - 12) / (x-4) = 3(x-4) / (x-4) = 3, x ≠ 4