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Unformatted text preview: Lecture 4 — Creating Functions We have now defined a good number of functions. How can we create more? From the graph of a function y = f ( x ) : Procedure New formula Illustration reflect across xaxis reflect across yaxis take absolute value Procedure New formula Illustration shift up or down shift right or left stretch or compress vertically stretch or compress horizontally y = 1 x y = 1 1 x y = e x y = 1 e x y = sin( x ) y = 3 sin(2 x ) y = ln( x ) y = 1 +  ln( x )  The graph of the function f ( x ) = x ln( x ) is shown. shift up 1 unit reflect over x axis reflect over x axis shift up 1 unit New Formula: New Formula: Even/Odd functions: If f ( x ) = f ( x ) for all x in the domain of f , If f ( x ) = f ( x ) for all x in the domain of f , Algebra of functions Suppose f and g are functions having domain A and B respectively. We define some new functions: Name Definition Domain f + g f g fg f g f ◦ g Examine the functions f ( x ) = ln( x ) g ( x ) = √ x h ( t ) = 1 t 2 Write the formula for each function below and list the domain. g f g ◦ f h ◦ g Piecewise functions We can build functions from portions of other func tions piece by piece by specifying which function corresponds to different x ....
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This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus

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