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Pre-Calc Homework Solutions 8

Pre-Calc Homework Solutions 8 - 8 Section 1.2 x 0 the...

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13. (a) Since we require 2 x $ 0, the domain is ( 2‘ , 0]. (b) [0, ) (c) [ 2 10, 3] by [ 2 1, 2] (d) None 14. (a) Since we require x 0, the domain is ( 2‘ , 0) < (0, ). (b) Note that } 1 x } can assume any value except 0, so 1 1 } 1 x } can assume any value except 1. The range is ( 2‘ , 1) < (1, ). (c) [ 2 4, 4] by [ 2 4, 4] (d) None 15. (a) Since we require 4 2 x 2 $ 0, the domain is [ 2 2, 2]. (b) Since 4 2 x 2 will be between 0 and 4, inclusive (for x in the domain), its square root is between 0 and 2, inclusive. The range is [0, 2]. (c) [ 2 4.7, 4.7] by [ 2 3.1, 3.1] (d) Symmetric about the y -axis (even) 16. (a) This function is equivalent to y 5 ˇ 3 x 2 w , so its domain is all real numbers. (b) [0, ) (c) [ 2 2, 2] by [ 2 1, 2] (d) Symmetric about the y -axis (even) 17. (a) Since we require x 2 0, the domain is ( 2‘ , 0) < (0, ) (b) Since } x 1 2 } . 0 for all x , the range is (1, ). (c) [ 2 4, 4] by [ 2 1, 5] (d) Symmetric about the y -axis (even) 18. (a) This function is equivalent to y 5 ˇ x 3 w , so its domain is [0, ). (b) [0, ) (c) [ 2 2, 5] by [ 2 2, 8] (d) None 19. Even, since the function is an even power of x .
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