1140 L10 - Lecture 10 part I Section 1.6 A Library of...

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Lecture 10, part I: Section 1.6 A Library of Functions 1. Linear Function f ( x ) = mx + b NOTE: There are two special types of linear functions: Constant Function ( f ( x ) = c ) and Identity Function ( f ( x ) = x ).
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2. Square Function f ( x ) = x 2 3. Cube Function f ( x ) = x 3 4. Square Root Function f ( x ) = p x
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5. Reciprocal Function f ( x ) = 1 x 6. Absolute Value Function f ( x ) = j x j A piecewise-de±ned function is de±ned by di²erent rules on di²erent parts of its domain. Graph a piecewise-de±ned 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 ² if it is open.
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ex. Sketch the graph of f ( x ) = 8 > < > : x 2 ; x < 1 1 ; 1 < x < 3 x; x ± 3
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Lecture 10, part II: Section 1.7 Transformations of Functions Vertical and Horizontal Translations Given y = f ( x ) and c > 0: To Graph: Shift f ( x ) f ( x ) + c f ( x ) ± c f ( x + c ) f ( x ± c ) NOTE: Numbers inside parentheses change the argument ( x -values):
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1140 L10 - Lecture 10 part I Section 1.6 A Library of...

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