Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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21.

Polynomial and Rational Functions yio &8 17. f(x)= (x- 1)4+ 2 18. f(x) <o o 19. f(x) (x +3)4-3 11 (x- 2)2+4 2 20. f(x) =x+ 1)3-3 Use an end behavior diagram, , the graph of each polynomial function. See Example 2. , or to describe the end behavior of 21. f(x) = 5x5 2x3 -3x + 4 22. f(x)=-x3 - 4x2 2x 1 23. f(x) =-4x3 + 3x2-1 24. f(x) 4x7 - x3-1 25. f(x) 9x6 - 3x4x2- 2 26. f(x) = 10x6 - x5 2x-2 27. f(x) 3 + 2x-4x2 - 5x10 28. f(x) 7 + 2x-5x2- 10x4 Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. 15 29. f(x) x3 5x2+2x- 8 30. f(x) =x3 +3x2- 13x 32. f(x) x(x + 1)(x- 1) 31. f(x) 2x(x- 3)(x +2) 34. f(x) x2(x-5) (x + 3)(x- 1) 33. f(x) x2(x - 2) (x + 3)2 11 36. f(x) (4x + 3) (x + 2)2 35. f(x) = (3x - 1)(x + 2)2 38. f(x)x+x36x- 36 37. f(x) x3 +5x2- x-5 11 40. f(x) 3x4+5x3- 2x2 1 39. f(x) x3- x2 - 2x 42. f(x) x2(x- 3)'(x + 1) 41. f(x) 2x3(x2 - 4) (x - 1) 2x4+ x3- 6x2- 7x- 2 44. f(x) 1 1 43. f(x) 2x3 - 5x2-x+6 46. f(x) =x4 + 3x3-3x2-11x - 6 3x4- 7x3-6x2+12x + 8 45. f(x) Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5 1
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Transcribed Image Text:Polynomial and Rational Functions yio &8 17. f(x)= (x- 1)4+ 2 18. f(x) <o o 19. f(x) (x +3)4-3 11 (x- 2)2+4 2 20. f(x) =x+ 1)3-3 Use an end behavior diagram, , the graph of each polynomial function. See Example 2. , or to describe the end behavior of 21. f(x) = 5x5 2x3 -3x + 4 22. f(x)=-x3 - 4x2 2x 1 23. f(x) =-4x3 + 3x2-1 24. f(x) 4x7 - x3-1 25. f(x) 9x6 - 3x4x2- 2 26. f(x) = 10x6 - x5 2x-2 27. f(x) 3 + 2x-4x2 - 5x10 28. f(x) 7 + 2x-5x2- 10x4 Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. 15 29. f(x) x3 5x2+2x- 8 30. f(x) =x3 +3x2- 13x 32. f(x) x(x + 1)(x- 1) 31. f(x) 2x(x- 3)(x +2) 34. f(x) x2(x-5) (x + 3)(x- 1) 33. f(x) x2(x - 2) (x + 3)2 11 36. f(x) (4x + 3) (x + 2)2 35. f(x) = (3x - 1)(x + 2)2 38. f(x)x+x36x- 36 37. f(x) x3 +5x2- x-5 11 40. f(x) 3x4+5x3- 2x2 1 39. f(x) x3- x2 - 2x 42. f(x) x2(x- 3)'(x + 1) 41. f(x) 2x3(x2 - 4) (x - 1) 2x4+ x3- 6x2- 7x- 2 44. f(x) 1 1 43. f(x) 2x3 - 5x2-x+6 46. f(x) =x4 + 3x3-3x2-11x - 6 3x4- 7x3-6x2+12x + 8 45. f(x) Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5 1
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