# review4 - MAC1140 Precalculus Algebra Summer B 2007 Review...

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MAC1140, Precalculus Algebra, Summer B 2007 Review Problems for Exam 4 1. Find the average rate of change of f ( x ) = x 3 - x over the interval [ - 3 , 1]. 2. For the function f ( x ) = 3 - | x + 3 | if x ≤ - 1 1 if - 1 < x 1 | x - 3 | - 1 if 1 < x . find all the (open) intervals where the function is decreasing, increasing and constant. Also find any local maximum and minimum. 3. Sketch all intermediate steps that are needed to graph the function (translating, flipping, stretching) starting from the basic function. a) f ( x ) = 2( x + 2) 2 + 1 b) f ( x ) = 1 - 1 2 | x | c) f ( x ) = 2 + - x 4. Sketch a graph of the following functions (find vertex and all inter- cepts): a) f ( x ) = 2( x +1) 2 - 3 b) f ( x ) = - 2 x 2 +8 x - 8 c) f ( x ) = x 2 - x - 6 5. What are the ranges of the following functions: a) f ( x ) = ( x - 2) 2 + 1 b) f ( x ) = - 2 x 2 + 8 x c) f ( x ) = 5 - 3 x + 2 6. A ball is thrown upward with initial velocity 80 feet per second and from a tower of height 96 feet. a) Find an expression for the height h ( t ) in terms of the time t in seconds.

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