hw1 - ECE320 Homework 1 Cornell University Spring 2006...

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ECE320 Homework 1 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the end of lecture on Tuesday, 7 February. Use only your assigned three-digit code and not your name. 1. (a) What is the domain, codomain, image, and graph( f ) of the usual quadratic polynomial x 2 - x + 2? (b) If a function f has the graph { (1 , a ) , (2 , b ) , ( - 1 , a ) , ( c, 0) } what are its domain and codomain? Can you evaluate f (0)? (c) Describe the domain and codomain for a color image created on your computer screen. (d) Provide an example of a non-constant function f having a domain of { a, * , & , ! } and a codomain of { 1 , 2 , b } . What is the image of your function? 2. (a) Given the logistic function f specified by graph( f ) = { ( x, y ) : x [0 , 1] , y = 3 x (1 - x ) } , plot its graph. (b) Plot the graph of the composition h = f ( f ) of the logistic with itself. 3. Is the “function” that is 0 on the irrational numbers and 1 on the rational numbers a function? If so, what are its domain, codomain, and graph? Can you plot this function?
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