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

This preview shows pages 1–12. Sign up to view the full content.

L3 – Mathematical Models and New Functions from Old Functions: Linear Functions Polynomial Functions Power Functions Rational Functions 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Root Functions Algebraic Functions Trigonometric Functions Inverse Trigonometric Functions Exponential Functions Logarithmic Functions 2
Vertical and Horizontal Shifts If c > 0, y = f ( x ) + c y = f ( x ) - c y = f ( x + c ) y = f ( x - c ) 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
y = | x + 1 | x + 1 Consider the graph of f ( x ) below. Sketch the graph of g (

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

### Page1 / 12

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

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online