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Pre-Calc Homework Solutions 38

# Pre-Calc Homework Solutions 38 - 38 Chapter 1 Review 39...

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34. (a) The function is defined for all values of x , so the domain is ( 2‘ , ). (b) The function is equivalent to y 5 ˇ 5 x 2 w , which attains all nonnegative values. The range is [0, ). (c) [ 2 8, 8] by [ 2 3, 3] 35. (a) The logarithm requires x 2 3 . 0, so the domain is (3, ). (b) The logarithm attains all real values, so the range is ( 2‘ , ). (c) [ 2 3, 10] by [ 2 4, 4] 36. (a) The function is defined for all values of x , so the domain is ( 2‘ , ). (b) The cube root attains all real values, so the range is ( 2‘ , ). (c) [ 2 10, 10] by [ 2 4, 4] 37. (a) The function is defined for 2 4 # x # 4, so the domain is [ 2 4, 4]. (b) The function is equivalent to y 5 ˇ ) x w ) w , 2 4 # x # 4, which attains values from 0 to 2 for x in the domain. The range is [0, 2]. (c) [ 2 6, 6] by [ 2 3, 3] 38. (a) The function is defined for 2 2 # x # 2, so the domain is [ 2 2, 2]. (b) See the graph in part (c). The range is [ 2 1, 1]. (c) [ 2 3, 3] by [ 2 2, 2] 39. First piece: Line through (0, 1) and (1, 0) m 5 } 0 1 2 2 1 0 } 5 } 2 1 1 } 5 2 1 y 5 2 x 1 1 or 1 2 x Second piece: Line through (1, 1) and (2, 0) m 5 } 0 2 2 2 1 1 } 5 } 2 1 1 } 5 2 1 y 5 2 ( x 2 1) 1 1 y 5 2 x 1 2 or 2 2 x f ( x ) 5 h 40. First piece: Line through (0, 0) and (2, 5) m 5 } 5 2 2 2 0 0 } 5 } 5 2 } y 5 } 5 2 } x Second piece: Line through (2, 5) and (4, 0) m 5 } 0 4 2 2 5 2 } 5 } 2 2 5 } 5 2 } 5 2 } y 5 2 } 5 2 } ( x 2 2) 1 5 y 5 2 } 5 2 } x 1 10 or 10
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