L03 - x ) = 2-f ( x ). 8 Algebra of Functions Let f and g...

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L3 – Mathematical Models and New Functions from Old Functions: Linear Functions Polynomial Functions Power Functions Rational Functions 1
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Root Functions Algebraic Functions Trigonometric Functions Inverse Trigonometric Functions Exponential Functions Logarithmic Functions 2
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Vertical and Horizontal Shifts If c > 0, y = f ( x ) + c y = f ( x ) - c y = f ( x + c ) y = f ( x - c ) 3
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Vertical and Horizontal Stretching and Reflecting If c > 1, y = cf ( x ) y = 1 c f ( x ) y = f ( cx ) y = f ( x c ) y = - f ( x ) y = f ( - x ) 4
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Sketch the graphs below: y = 1 x y = 1 x - 1 y = x 2 y = x 2 + 4 y = x 3 y = ( x + 1) 3 5
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Sketch the graphs below: y = x y = 2 + x - 1 y = x 1 3 y = - x 1 3 y = sin( x ) y = 1 3 sin( x ) 6
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Sketch the graphs below: y = cos( x ) y = - 2cos( x - π 2 ) y = 1 + sin(2 x ) y = sin( 1 3 x ) y = sin( - x ) y = | sin( 1 3 x ) | 7
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y = | x + 1 | x + 1 Consider the graph of f ( x ) below. Sketch the graph of g (
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Unformatted text preview: x ) = 2-f ( x ). 8 Algebra of Functions Let f and g be functions with domains A and B respectively, then Function Domain ( f + g )( x ) = ( f-g )( x ) = ( fg )( x ) = ( f g )( x ) = 9 If f ( x ) = 1 x and g ( x ) = √ x-1, find ( f + g )( x ) and ( fg )( x ) and their domains. 10 Composition of Functions ( f ◦ g )( x ) = Domain ( g ◦ f )( x ) = Domain 11 If f ( x ) = 1 x and g ( x ) = √ x-1, find the composites f ◦ g and g ◦ f and their domains. If h ( x ) = x 2 , find h ◦ g ◦ f and its domain. 12...
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L03 - x ) = 2-f ( x ). 8 Algebra of Functions Let f and g...

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