mt-3sum07

# mt-3sum07 - 1. (15 points) (a) Give a decent sketch of the...

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1. (15 points) (a) Give a decent sketch of the graph of the following functions. Don’t forget to supply all the requested information such as intercepts, vertex, etc. (1) f ( x )=1 - x 2 x -intercept(s): y -intercept: Coordinates of vertex: (2) f ( x )= x 2 + x - 2 x -intercept(s): y -intercept: Coordinates of vertex: (b) Which of the following graphs represents y as a function of x ? 1

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2. (15 points) Consider the function f ( x ) = ( x - 1) 3 +1 (a) (5 points) Sketch the graph of f ( x ) and use it to argue that f ( x ) has an inverse function. (b) (5 points) Find the equation for f - 1 ( x ) (c) ( 5 points) Sketch the graph of f - 1 ( x ) in the same coordinate system from above. How are the graphs of f ( x ) and f - 1 ( x ) related? 2
f ( x ) such that f (2) = - 3 and f (6) = - 5. 4. (15 points) Two real numbers add to 40. (a) Find the minimal value of the sum of the squares of the two numbers. (b) Why does the answer you found correspond to a minimal value and not a maximal

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## This note was uploaded on 08/09/2011 for the course MATH 3 taught by Professor Staff during the Spring '08 term at UCSC.

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mt-3sum07 - 1. (15 points) (a) Give a decent sketch of the...

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