Algebraic For the following exercises, find the domain of the rational functions. 6. f (x) = x-1 x+2 7. f(x) = x+1 x2-1 8. f(x) = x2+4 x2-2x-8 9. f (x) = *+4x-3 x4-5x2+4 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. 10. f (x) = X- I 11. f (x) = 2 12. f (x) = X 2 - 9 13. f (x) = 2+5x-36 X 14. f (x) = 3+x x3-27 15. f (x) = 3x-4 x3-16x 16. f(x) = x2-1 x3+9x2+14x 17. f(x) = x+5 x2-25 18. f(x) = x-4 19. f (x) = 4-2x 3 x- 1For the following exercises, find the x- and y-intercepts for the functions. 20. f (x) = x+5 x2+4 21. f ( x) = x x 2 - x 22. f (x) = x2+8x+7 x2+11x+30 23. f (x) = x2+x+6 x2-10x+24 24. f (x) = 94-2x2 3x2-12 For the following exercises, describe the local and end behavior of the functions. 25. f (x) = 2 X 2 x+ 1 26. f (x) = 2x x- 6 27. f (x) = -2x x - 6 28. f (x) = x2-4x+3 x2-4x-5 29 . f (x ) = 6x2+13x-5For the following exercises, write an equation for a rational function with the given characteristics. 51. Vertical asymptotes at x = 5 and x = -5, x-intercepts at (2, 0) and (-1, 0), y-intercept at (0, 4) 52. Vertical asymptotes at x = -4 and x = -1, x-intercepts at (1, 0) and (5, 0) , y-intercept at (0, 7) 53. Vertical asymptotes at x = -4 and x = -5, x-intercepts at (4, 0) and (-6, 0) , Horizontal asymptote at y = 7 54. Vertical asymptotes at x = -3 and x = 6, x-intercepts at (-2, 0) and (1, 0) , Horizontal asymptote at y = -2 55. Vertical asymptote at x = -1, Double zero at x = 2, y-intercept at (0, 2) 56. Vertical asymptote at x = 3, Double zero at x = 1, y-intercept at (0, 4) 56. Vertical asymptote at x = 3, Double zero at x = 1, y-intercept at (0, 4)For the following exercises, use the graphs to write an equation for the function. 57. NODOT ....... -7 -6 -5-4 -3 -2 -10 12345 X