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# L10 - Lecture 10 part I Section 1.6 of Functions 1 Linear...

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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 ).

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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.

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ex. Sketch the graph of u1D453 ( u1D465 ) = u1D465 2 , u1D465< 1 1 , 1 <u1D465< 3 u1D465, u1D465 3
Lecture 10, part II: Section 1.7 Transformations of Functions Vertical and Horizontal Translations Given u1D466 = u1D453 ( u1D465

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