This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 12: Changing coordinates and transforming graphs June 17, 2010 Introduction Suppose ( x,y ) is a statement in which the variables x and y appear. For example, ( x,y ) might be the statement x 2 + y 2 = 35 2 . It could also be a more complicated statement, such as: x 2 + y 2 = 35 2 and y = 2 3 ( x + 1) , or x 2 + y 2 = 35 2 and x and y are both rational . No matter how complicated ( x,y ) is, by the graph of ( x,y ), we mean the set of all number pairs for which ( x,y ) is true. If we interpret number pairs as points by referring to the standard x ycoordinate system on the plane, then the graph of ( x,y ) is a set of points in the plane. 1 We will use the symbol X to denote the graph: X := { ( x,y )  ( x,y ) } . Now, suppose a and b are any numbers. Consider the set X := { ( x,y )  ( x a,y b ) } . I assert that X coincides with the set of all pairs obtained by taking a pair belonging to X and adding ( a,b ) to it. In other words, X is the image of X after a translation by ( a,b ). We can demonstrate this assertion as follows: ( ( x + a ) , ( y + b ) ) X ( ( x + a ) a, ( y + b ) b ) ( x ,y ) ( x ,y ) X Returning to the example of the circle,...
View
Full
Document
This note was uploaded on 11/23/2011 for the course MATH 6302 taught by Professor Madden during the Summer '11 term at LSU.
 Summer '11
 MADDEN
 Math

Click to edit the document details