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MT1_P - Stony Brook University Mathematics Department B...

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Stony Brook University Calculus A Mathematics Department MAT 125 B. Andersen, C. Curry, M. Mazin, J. Viro October 5, 2010 Review Sheet for Midterm 1 No electronic devices, books or notes allowed. Show all work. Circle your final answers. 1. For the function f ( x ) = ( x - 2) 2 evaluate the following a) f ( a + 1) b) f ( x + h ) - f ( x ) h 2. Find the domain of the following functions: a) x - 2 + 5 x - 14 b) 16 2 x - 8 c) ln (2 x + 1) d) e x - 3 · sin x 3. Write the function whose graph is the line segment with endpoints (2 , - 1) and (4 , 3). 4. For the function f ( x ) = ( x, 0 x 4 - x + 6 , 4 < x 6 a) Sketch its graph. b) State its domain and range. 5. Given the graph of the function g ( x ), sketch the graphs of the functions below: a) g ( x - 1) b) g ( x ) - 1 c) - g ( x ) + 2 d) 1 2 g ( x ) + 1 e) g (2 x )
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2 6. Let f ( x ) = x and g ( x ) = x 2 - 4. Find an expression for each of the following functions and give their domains: a) ( f + g )( x ) b) ( f g )( x ) c) f g ( x ) d) ( g g )( x ) 7. Let h ( x ) = ln x . Write an equation of the graph that result from the following transformation and sketch the graph.
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