By Mark Dugopolski
Algebra for students, 4th version, is designed to supply scholars with the algebra history wanted for extra college-level arithmetic classes. The unifying subject of this article is the advance of the abilities beneficial for fixing equations and inequalities, by means of the appliance of these talents to fixing utilized difficulties. this article comprises 2 chapters, Polynomial & Rational capabilities, and Counting & likelihood, as well as these present in Dugopolski's Intermediate Algebra.
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Extra resources for Algebra for College Students, 5th Edition
7. 10. answer. is not a member of is not a subset of not equal intersection A ϭ ͕x Ϳ x is a counting number͖ The set B has an infinite number of elements. The set of counting numbers less than 50 million is an infinite set. 1ʦAʝB 5. 3 ʦ A ʜ B 6. A ʝ B ϭ C CʕB 8. A ʕ B 9. com! > Practice Problems > NetTutor > Self-Tests > e-Professors > Videos Exercises U Study Tips V • Exercise sets are designed to increase gradually in difficulty. So start from the beginning and work lots of exercises. • Find a group of students to work with outside of class.
7 Q 58. 8 61. 0 63. ͕2, 3͖ 65. ͕3, ͙2ෆ ͖ R 62. 0 I R 77. 3 4 5 6 7 8 9 78. 3 4 5 6 7 8 9 Q I Q 64. ͕0, 1͖ Q 76. The set of real numbers greater than 2 and less than or equal to 5. Write the interval notation for the interval of real numbers shown in each graph. Z 60. ͙2 ෆ R 75. The set of real numbers greater than or equal to 1 and less than 3 in each blank so that 45. N ෆ 59. ͙2 72. The set of real numbers between Ϫ1 and 3 66. ͕3, ͙2 ෆ͖ 79. Ϫ4Ϫ3Ϫ2Ϫ1 0 1 2 N Q U5V Intervals of Real Numbers Write each interval of real numbers in interval notation and graph it.
E X A M P L E 6 Combining intervals Write each union or intersection as a single interval. a) (2, 4) ʜ (3, 6) b) (2, 4) പ (3, 6) c) (Ϫ1, 2) ഫ [0, ϱ) d) (Ϫ1, 2) പ [0, ϱ) Solution a) Graph (2, 4) and (3, 6) as in Fig. 26 on the next page. The union of the two intervals consists of the real numbers between 2 and 6, which is written as (2, 6). qxd 10/31/07 6:37 PM Page 16 16 1-16 Chapter 1 The Real Numbers b) Examining the graphs in Fig. 26, we see that only the real numbers between 3 and 4 belong to both (2, 4) and (3, 6).
Algebra for College Students, 5th Edition by Mark Dugopolski