Determine whether each function can be obtained from the parent function, y = x n , y equals , x to the n , comma  using basic transformations. If so, describe the sequence of transformations.

28. y = 3 x 3 y equals , 3 x cubed
29. y = 2 ( x − 3 ) 2 + 5 y equals . 2 open x minus 3 close squared . plus 5
30. y = x 3 − x y equals , x cubed , minus x
31. y = x 2 − 8 x + 7 y equals , x squared , minus 8 x plus 7
32. y = ( x + 2 ) 4 y equals . open x plus 2 close to the fourth
33. y = − 4 x 3 y equals negative 4 , x cubed

Determine the transformations that were used to change the graph of the parent function y = x 3 y equals , x cubed  to each of the following graphs.

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40. Physics The formula K = 1 2 m v 2 k equals , 1 half , m , v squared  represents the kinetic energy of an object. If the kinetic energy of a ball is 10  lb-  ft  2 / s 2 10 , lbminus . ft squared , slash , s squared  when it is thrown with a velocity of 4  ft/s , 4 , ftslashs , comma  how much kinetic energy is generated if the ball is thrown with a velocity of 8 ft/s?
41. Reasoning Explain why the basic transformations of the parent function y = x 5 y equals , x to the fifth  will only generate functions that can be written in the form y = a ( x − h ) 5 + k . y equals . eh open x minus h close to the fifth . plus k .
42. Reasoning Explain why some quartic polynomials cannot be written in the form y = a ( x − h ) 4 + k . y equals . eh open x minus h close to the fourth . plus k .  Give two examples.

43. Error Analysis Your friend claims he can write any cubic polynomial as the sum of two functions: (1) a cubic monomial and (2) a transformation of y = x 2 . y equals , x squared , .  Explain why your friend's claim is incorrect.

    
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