L10 - Lecture 10 part I Section 1.6 A Library of Functions...

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Unformatted text preview: Lecture 10, part I: Section 1.6 A Library of Functions 1. Linear Function u1D453 ( u1D465 ) = u1D45Au1D465 + u1D44F NOTE: There are two special types of linear functions: Constant Function ( u1D453 ( u1D465 ) = u1D450 ) and Identity Function ( u1D453 ( u1D465 ) = u1D465 ). 2. Square Function u1D453 ( u1D465 ) = u1D465 2 3. Cube Function u1D453 ( u1D465 ) = u1D465 3 4. Square Root Function u1D453 ( u1D465 ) = √ u1D465 5. Reciprocal Function u1D453 ( u1D465 ) = 1 u1D465 6. Absolute Value Function u1D453 ( u1D465 ) = ∣ u1D465 ∣ A piecewise-defined function is defined by different rules on different parts of its domain. Graph a piecewise-defined function 1. Divide the domain of the function into parts. 2. Graph separately each branch of the correspond- ing parts of the domain. 3. On each branch of the graph, draw end points as a solid dot ∙ if the interval is closed on that side and as ∘ if it is open. ex. Sketch the graph of u1D453 ( u1D465 ) = ⎧ ⎨ ⎩ u1D465 2 , u1D465 < 1 1 , 1 < u1D465 < 3 u1D465, u1D465 ≥ 3 Lecture 10, part II: Section 1.7Lecture 10, part II: Section 1....
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This note was uploaded on 12/02/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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L10 - Lecture 10 part I Section 1.6 A Library of Functions...

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