L04 - Lecture 4 — Creating Functions We have now defined...

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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 x-axis reflect across y-axis 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.

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L04 - Lecture 4 — Creating Functions We have now defined...

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