1. {−5,0,5,10,15}
2. (−∞,∞)
3. (−∞,21)∪(21,∞)
4. [−25,∞)
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∣x≤−2or−1≤x<3};
(−∞,−2]∪[−1,3)
6. Domain = [1950, 2002] Range = [47,000,000, 89,000,000]
7. Domain: (−∞,2] Range: (−∞,0]
8.
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)=3x 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. (−∞,−21)∪(−21,∞)
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,−61]∪[61,6] Range: [−6,−61]∪[61,6]
37. Domain: [−3,∞) Range: [0,∞)
39. Domain: (−∞,∞)
41. Domain: (−∞,∞)
43. Domain: (−∞,∞)
45. Domain: (−∞,∞)
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]
Window: [0.1,0.5] Range: [4,100]
57. [0,8]
59. Many answers. One function is f(x)=x−21.
61. The domain is [0,6]; it takes 6 seconds for the projectile to leave the ground and return to the ground.
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Precalculus.Provided by: OpenStaxAuthored by: Jay Abramson, et al..Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions.License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..