09.12 - [Go around with names[Hand out time sheets Section 1.2 What's the main point of section 1.2 Functions that crop up in the real world can be

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[Go around with names] [Hand out time sheets] Section 1.2 What’s the main point of section 1.2? ..?. . Functions that crop up in the real world can be represented or at least approximated by functions that are algebraically built up from some universal building blocks. If we can understand the building blocks, we can understand the functions that are built from them, and their graphs. Building blocks: linear functions, polynomials, rational functions (built from polynomials), trig and exponential functions, and logarithms. Combination rules: You can add, subtract, multiply, or divide two functions to get a new function; or you can compose two functions to get a new function. ( f + g )( x ) = f ( x )+ g ( x ) ( f g )( x ) = f ( x ) – g ( x ) ( f g )( x ) = f ( x ) g ( x ) ( f / g )( x ) = f ( x )/ g ( x )
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( f ° g )( x ) = f ( g ( x )) Q. Is there a way to express y =| x | in terms of standard algebraic operations, as a single algebraic expression? ..?. . A. sqrt( x 2 ) Q. Is there an algebraic function whose value is +1 for positive values of x and –1 for negative values of x ? ... A. (sqrt( x 2 ))/ x . Q. (continuation of preceding question) Is there an algebraic function whose value is +1 for positive values of x , –1 for negative values of x , and 0 for x =0? ..?. . A. To be continued!
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This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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09.12 - [Go around with names[Hand out time sheets Section 1.2 What's the main point of section 1.2 Functions that crop up in the real world can be

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