quiz1sol - G x = 4 if x> 2 if x< And the graph is shown...

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Quiz 1 MATH 1013 SOLUTION NAME (print): (Family) (Given) STUDENT NUMBER: 1.(10pts) Find the domain and sketch the graph of the func- tion G ( x ) = 3 x + j x j x SOLUTION: This is question 39 from section 1.1. The domain is the set of all values of x where G ( x ) is de ned. The only value at which it is not de ned is when x = 0 ( 0 0 is not de ned). So the domain is ( 1 ; 0) [ (0 ; 1 ) . To nd the graph of y = G ( x ) , it helps to rst simplify the expression 3 x + j x j x using the de nition j x j = ( x if x 0 , x if x < 0 . So G ( x ) = ( 3 x + x x if x > 0 , 3 x x x if x < 0 .
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Simplifying gives
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Unformatted text preview: G ( x ) = ( 4 if x > , 2 if x < . And the graph is shown at the solutions section of the textbook. 2.(10pts) Calculate the exact value of each of the following (1) sin 4 ± 3 = ± p 3 2 (2) tan 4 ± 3 = p 3 (3) csc 4 ± 3 = ± 2 p 3 This can be seen by noting the position angle 4 ± 3 in the 3rd quadrant and the basic triangle with sides ± 1 2 ; p 3 2 and hypotenuse of length 1 ....
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