Solutions

Solutions to Try Its

1. {5,0,5,10,15}

2. (,)

3. (,12)(12,)

4. [52,)

5. values that are less than or equal to –2, or values that are greater than or equal to –1 and less than 3;
{x|x2or1x<3}; (,2][1,3)

6. Domain = [1950, 2002]   Range = [47,000,000, 89,000,000]
7. Domain: (,2]   Range: (,0]
8.
Graph of f(x).

 

Solutions for Odd-Numbered Section Exercises

1. The domain of a function depends upon what values of the independent variable make the function undefined or imaginary.

3.  There is no restriction on x for f(x)=x3 because you can take the cube root of any real number. So the domain is all real numbers, (,). When dealing with the set of real numbers, you cannot take the square root of negative numbers. So x -values are restricted for f(x)=x to nonnegative numbers and the domain is [0,).

5. Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the x -axis and y -axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpoints with an open circle. Use an arrow to indicate or  . Combine the graphs to find the graph of the piecewise function.

7. (,)

9. (,3]

11. (,)

13. (,)

15. (,12)(12,)

17. (,11)(11,2)(2,)

19. (,3)(3,5)(5,)

21. (,5)

23. [6,)

25. (,9)(9,9)(9,)

27. Domain: (2,8]   Range [6,8)

29. Domain: [4,4]   Range: [0,2]

31. Domain: [5, 3)   Range: [0,2]

33. Domain: (,1]   Range: [0,)

35. Domain: [6,16][16,6]   Range: [6,16][16,6]

37. Domain: [3, )   Range: [0,)

39. Domain: (,)

Graph of f(x).

41. Domain: (,)

Graph of f(x).

43. Domain: (,)

Graph of f(x).

45. Domain: (,)

Graph of f(x).

47. {f(3)=1;f(2)=0;f(1)=0;f(0)=0

49. {f(1)=4;f(0)=6;f(2)=20;f(4)=34

51. {f(1)=5;f(0)=3;f(2)=3;f(4)=16

53. Domain: (,1)(1,)

55. Window: [0.5,0.1]   Range: [4, 100]

Graph of the equation from [0.1, 0.5].

Window: [0.1, 0.5]   Range: [4, 100]

Graph of the equation from [0.1, 0.5].

57. [0, 8]

59. Many answers. One function is f(x)=1x2.

61. The domain is [0, 6]; it takes 6 seconds for the projectile to leave the ground and return to the ground.