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Graph f(x)

By anthonycira

Added: April 22, 2009 18:55:55

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Graph f(x)

Graph f(x)
1 f(x)
1.1 Domain
1.2 Range
1.3 Symmetry
1.3.1 Even Function
1.3.1.1 Symmetric about the y-axis
1.3.1.1.1 f(-x)=f(x)
1.3.2 Odd Function
1.3.2.1 Symmetric about the origin
1.3.2.1.1 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
1.5.1.1 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
2.1.1.1 Increasing Intervals
2.1.1.1.1 f'(x)>0
2.1.1.2 Decreasing Intervals
2.1.1.2.1 f'(x)<0
2.1.1.3 The First Derivative Test
2.1.1.3.1 f'(x) changes sign from + to -
2.1.1.3.1.1 Local Max
2.1.1.3.2 f'(x) changes sign from - to +
2.1.1.3.2.1 Local Min
3 f''(x)
3.1 The Second Derivative Test
3.1.1 f'(c)=0 or f'(c) is UND
3.1.1.1 f''(c)>0
3.1.1.1.1 Local Min at c
3.1.1.2 f''(c)<0
3.1.1.2.1 Local Max at c
3.1.1.3 f''(c)=0
3.1.1.3.1 Can't say anything
3.1.1.3.1.1 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
3.2.1.1 Concave Up Interval
3.2.1.1.1 f''(x)>0
3.2.1.2 Concave Down Interval
3.2.1.2.1 f''(x)<0
3.2.1.3 Points of Inflection
3.2.1.3.1 f'' changes sign