Graph f(x)

Add by Anthony Cira | Apr 22, 2009 18:55  1157 |  1
Graph f(x)

Map Outline

Graph f(x)
1 f(x)
1.1 Domain
1.2 Range
1.3 Symmetry
1.3.1 Even Function Symmetric about the y-axis f(-x)=f(x)
1.3.2 Odd Function Symmetric about the origin f(-x)=-f(x)
1.4 Horizontal Asymptotes
1.4.1 Take Limit of f(x) as x-> Infinity/-Infinity
1.5 Vertical Asymptotes
1.5.1 Find out where f(x) is undefined Take a limit as x approaches the undefined number
1.6 Holes (discontinutities)
1.6.1 Factor f(x) and see if terms cancel out on the numerator and denominator
1.7 x-intercepts
1.7.1 Factor f(x) and solve f(x)=0
1.8 y-intercept
1.8.1 Set x=0 in f(x) and solve for y
2 f'(x)
2.1 Find Critical Numbers of f'(x)
2.1.1 Make a Chart Increasing Intervals f'(x)>0 Decreasing Intervals f'(x)<0 The First Derivative Test f'(x) changes sign from + to - Local Max f'(x) changes sign from - to + Local Min
3 f''(x)
3.1 The Second Derivative Test
3.1.1 f'(c)=0 or f'(c) is UND f''(c)>0 Local Min at c f''(c)<0 Local Max at c f''(c)=0 Can't say anything Use the First Derivative Test to check to see if Local Max/Min at c
3.2 Find Critical Numbers of f''(x)
3.2.1 Make a Chart Concave Up Interval f''(x)>0 Concave Down Interval f''(x)<0 Points of Inflection f'' changes sign

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