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quiz4solutions

# quiz4solutions - stays the same when a(horizontal vertical...

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MAC1147: Quiz #4 09/22/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are finished, FOLD your paper in half lengthwise and write your name on the back. 1. In the following questions, x 1 , x 2 , and c are real numbers. (a) State the definition of the average rate of change of f ( x ) from x 1 to x 2 . Δ y Δ x = f ( x 2 ) - f ( x 1 ) x 2 - x 1 (b) Find the average rate of change of f ( x )+ c from x 1 to x 2 . f ( x 2 ) + c - [ f ( x 1 ) + c ] x 2 - x 1 = f ( x 2 ) - f ( x 1 ) x 2 - x 1 (c) Use your answers to parts a and b to complete the statement of the following theorem: “The average rate of change of a function (increases/decreases/
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Unformatted text preview: stays the same ) when a (horizontal/ vertical ) translation is applied to it.” 2. Let f ( x ) = x 2 . (a) Sketch a graph of f ( x ) . Label any intercepts. (See #2 in the Library of Functions from Lecture 10, Part I) (b) Sketch a graph of f ( x ) + 1 . Label any intercepts. (This is f ( x ) shifted up by 1. There is a y-intercept at (0 , 1) .) (c) Sketch a graph of f ( x + 1) . Label any intercepts. (This is f ( x ) shited left by 1. There is a y-intercept at (0 , 1) and an x-intercept at (-1 , 0) .) 1...
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