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Unformatted text preview: 1. (20 points) 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. (a) f ( x ) = 1- x 2 x-intercept(s): y-intercept: Coordinates of vertex: (b) f ( x ) = ( x- 2) 2 ( x + 1) x-intercept(s): y-intercept: Coordinates of vertex: (c) g ( x ) = 3- x + 1 x-intercept(s): y-intercept: equation of asymptote: (d) g ( x ) = log 2 ( x- 2)- 1 x-intercept(s): y-intercept: equation of asymptote: 1 2. (15 points) Consider the function f ( x ) = 5 x 3 + 3 (a) (4 points) Sketch the graph of f ( x ) (b) (3 points) Show that the function f ( x ) has an inverse function f- 1 ( x ). Hint: You can do this algebraically OR graphically (c) (4 points) Find the equation for f- 1 ( x ) (d) (4 points) Sketch the graph of f- 1 in the same coordinate system. How are the graphs of f ( x ) and f- 1 ( x ) related? 3. (10 points) Find the linear function f ( x ) such that f (- 1) = 0 and f (5) = 4....
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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.
- Spring '08