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Additional Problems Problem 1a 32 ( ) 4 4 1 : : 1 : 1, , 1 4 :1 & 1 : 2 2 3 12 : 23 f x x x x Domain x Range y Zeros x x x y intercept y Relative maximum minimum points on graph No asymptotes Function is increasing x and x Function is decreasing x End behavoi                     :, , r as x y as x y         -3 -2 -1 1 2 3 4 -9 -8 -7 -6 -5 -4 1 2 3 4 5 6 7 8 9 x y 2 , 0.926 3 Relative minimum    19 , 24 Relative maximum

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Problem 1b 4 3 2 ( ) 4 5 3 f x x x x x 4 3 2 ( ) 4 5 3 : : : 1, 3 :3 : (2.035, 21.018) : 2.035 : f x x x x x Domain x Range y Real zeros x x Complex zeros see below on page y intercept y Relative minimum No asymptotes Function is increasing x Function is decreasing                 2.035 :, , x End behavoir as x y as x y           
4 3 2 3 2 2 2 2 2 2 11 4 : ( ) 4 5 3 ( 3)( 2 2 1) 0 ( 3)( 1)( 0 1 0 : : 10 1 1 1 2 4 If we were to show the linear factors f x x x x x x x x x x x x x The final factor x x will yield the complex roots Solving by completing the square xx x                  2 3 4 13 24 22 2 x x i x

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