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Pre-Calc Homework Solutions 9

# Pre-Calc Homework Solutions 9 - Section 1.2 32(a 44 Line...

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32. (a) [ 2 4, 4] by [ 2 2, 3] (b) ( 2‘ , ) or all real numbers (c) [0, ) 33. (a) [ 2 3.7, 5.7] by [ 2 4, 9] (b) ( 2‘ , ) or all real numbers (c) ( 2‘ , ) or all real numbers 34. (a) [ 2 2.35, 2.35] by [ 2 1, 3] (b) ( 2‘ , ) or all real numbers (c) [0, ) 35. Because if the vertical line test holds, then for each x -coordinate, there is at most one y -coordinate giving a point on the curve. This y -coordinate would correspond to the value assigned to the x -coordinate. Since there is only one y -coordinate, the assignment would be unique. 36. If the curve is not y 5 0, there must be a point ( x , y ) on the curve where y 0. That would mean that ( x , y ) and ( x , 2 y ) are two different points on the curve and it is not the graph of a function, since it fails the vertical line test. 37. No 38. Yes 39. Yes 40. No 41. Line through (0, 0) and (1, 1): y 5 x Line through (1, 1) and (2, 0): y 5 2 x 1 2 f ( x ) 5 h 42. f ( x ) 5 h 43. Line through (0, 2) and (2, 0): y 5 2 x 1 2 Line through (2, 1) and (5, 0): m 5 } 0 5 2 2 1 2 } 5 } 2 3 1 } 5 2 } 1 3 } , so y 5 2 } 1 3 } ( x 2 2) 1 1 5 2 } 1 3 } x 1 } 5 3 } f ( x ) 5 h 44. Line through ( 2 1, 0) and (0, 2 3): m 5 } 0 2 2 3 ( 2 2 0 1) } 5 }
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