# soln1 - ECE320 Solution Notes to Homework 1 Cornell...

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ECE320 Solution Notes to Homework 1 Spring 2006 Cornell University T.L.Fine 1. (a) What is the domain, codomain, image, and graph( f ) of the usual quadratic polynomial x 2 - x + 2? In the usual case the domain D is the set R of real numbers and the codomain R is often taken as the same set. The image set I , however, is a proper subset of the codomain in this case. This quadratic can take on all sufficiently large positive values as the highest power term has a positive coefficient. However, it cannot take on all values. Its minimum value is determined by setting d ( x 2 - x + 2) dx = 2 x - 1 = 0 , which locates the minimizing argument at x = 0 . 5 and the minimum value of the function at 0 . 25 - 0 . 5 + 2 = 1 . 75. We conclude that I = [1 . 75 , ) R . Finally, graph( f ) = { ( x, y ) : x R , y = 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)? D = { 1 , 2 , - 1 , c } , R = { a, b, 0 } . As 0 / ∈ D , f (0) is undefined. (c) Describe the domain and codomain for a color image created on your computer screen. In my case D = { ( x, y ) : 1 x 1680 , 1 y 1050 } , R = { ( r, g, b ) : 0 r 2 8 - 1 = 255 , 0 g 255 , 0 b 255 } . (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?

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