CalcNotes0101-page6

CalcNotes0101-page6 - , which is read the set of all real...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
(Chapter 1: Review) 1.06 The resulting range of f is the set of all nonnegative real numbers R ± 0 (i.e., all real numbers that are greater than or equal to 0), because every such number is the square of some real number. Warning : Squares of real numbers are never negative. This fact comes in very handy throughout math. The graph of the range is: The filled-in circle serves to include 0 in the range. We could also use a left bracket (“[”) here instead of a filled-in circle; the bracket opens towards the shading. The graph helps us figure out the interval form In interval form , the range is 0, ± ² ³ ) . We have a bracket next to the 0, because 0 is included in the range. In set-builder form , the range is: y ± R y ² 0 {} , or y ± R : y ² 0 {}
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , which is read the set of all real values y such that y . Using y instead of x is more consistent with our graphing conventions, and it helps us avoid confusion with the domain. Note: denotes set membership. Technical Note : We say that f maps the domain R to the codomain R , or that f maps R to itself. Using notation, we write f : R R . This is because f assigns a real number output (i.e., a member of the codomain) to each real number input in the domain. The range is a subset of the codomain. In fact, here, the range is a proper subset of the codomain, because not every real number in the codomain is assigned. In particular, the negative reals are not assigned....
View Full Document

This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

Ask a homework question - tutors are online