soln1 - ECE320 Solution Notes to Homework 1 Spring 2006...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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- . 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, } . 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 , g 255 , 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?...
View Full Document

This homework help was uploaded on 09/25/2007 for the course ECE 3200 taught by Professor Fine during the Spring '06 term at Cornell University (Engineering School).

Page1 / 6

soln1 - ECE320 Solution Notes to Homework 1 Spring 2006...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online