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

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(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 {}
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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....
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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.

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