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This Elibron Classics e-book is a facsimile reprint of a 1904 version via Adam and Charles Black, London.
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This Elibron Classics ebook is a facsimile reprint of a 1863 variation by means of Macmillan and Co. , Cambridge - London.
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Additional info for Algebra: An Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges. Part 1
F x 4 x 5 if if 5 x if 23. f x 3 if x 2 if x0 x2 x2 0 x3 x3 3 4 x if 22. f x x 1 if x 3 1 if 24. 2 Domain and Range 33 Write a formula for the piecewise function graphed below. 25. 26. 27. 28. 29. 30. Sketch a graph of each piecewise function x if x 2 31. f x 5 if x 2 4 32. f x x x2 if 33. f x x 2 if x 1 if 34. f x 3 if x if 3 35. f x x 1 if 3 if x0 x0 x 2 2 x 1 x 1 if x0 if x0 3 if 36.
A more compact alternative to set-builder notation is interval notation, in which intervals of values are referred to by the starting and ending values. Curved parentheses are used for “strictly less than”, and square brackets are used for “less than or equal to”. The table below will help you see how inequalities correspond to set-builder notation and interval notation: Inequality 5 h 10 Set Builder Notation h | 5 h 10 Interval notation (5, 10] 5 h 10 h | 5 h 10 h | 5 h 10 h | h 10 h | h 10 h | h R [5, 10) 5 h 10 h 10 h 10 all real numbers (5, 10) (,10) [10, ) (, ) To combine two intervals together, using inequalities or set-builder notation we can use the word “or”.
G ( x) 2 x 2 9 on [4, b] 13. h( x) 3 x 4 on [2, 2+h] 14. k ( x) 4 x 2 on [3, 3+h] 1 on [9, 9+h] t4 17. j ( x) 3x 3 on [1, 1+h] 1 on [1, 1+h] x3 18. r (t ) 4t 3 on [2, 2+h] 19. f ( x) 2 x 2 1 on [x, x+h] 20. g ( x) 3x 2 2 on [x, x+h] 15. a (t ) 16. 3 Rates of Change and Behavior of Graphs 47 For each function graphed, estimate the intervals on which the function is increasing and decreasing. 21. 22. 23. 24. For each table below, select whether the table represents a function that is increasing or decreasing, and whether the function is concave up or concave down.