6. Sophisticated Graphing

1
6. Sophisticated Graphing

• In graphing functions, there is following
  procedure will be helpful in most cases
• Check Df
• Test for symmetry (odd or even function)
• First derivative ? critical points? inc or dec?
• Local max-min
• Second derivative? concave up/downward,
  inflection points
• Asymtot
• Plot a few points
• Sketch the graph

2
Asymtot

• A line is vertical asymtot from a
  function is one of the statements
  bellow is correct

3
Horizontal Asymtot
A line is horizontal asymtot from a
function yf(x) if
4
Back to an example

• Is the function have a vertical and horizontal
  asymtot?

5

• What about this ones?

6
Exercise (1)
Next Question How does the graph wiggle between
the two ends ?
Frame look at back the step to Graph the
function!
Starts here
Ends here
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Derivative



2nd derivative




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Decreasing Concave down
Decreasing Concave up
Increasing Concave down
Decreasing Concave up
Decreasing Concave down
Starts here
Increasing Concave up
Local max
Ends here
A twist Concavity changes a point of
inflection
A twist Concavity changes a point of
inflection
A twist Concavity changes a point of
inflection
Graph rebounds after a dip a local min
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Exercise (2)
Next Question How does the graph wiggle within
each of the three sections ?
Sketch
Frame
?
?
?
Domain
?
?
Asymptotes
?
?
?
Starts here
Ends here
?
?
?
10
Wiggle
Derivative
2nd derivative
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Example (3)
Next Question How does the graph wiggle within
each of the three sections ?
Sketch
Frame
?
?
?
?
?
Domain
?
?
Asymptotes
?
Starts here
Ends here
?
?
?
12
Wiggle
Derivative
2nd derivative
13
Example (4)
Sketch
Frame
Next Question How does the graph wiggle between
the two ends ?
?
Domain
Ends here
Asymptotes
?
?
Starts here
14
Wiggle
Derivative
2nd derivative
15
Example (5)
Sketch
?
Frame
Next Question How does the graph wiggle within
the two regions ?
?
?
Domain
Ends here
Asymptotes
?
?
Starts here
?
16
Wiggle
Derivative
2nd derivative
17
Example (6)
Next Question How does the graph wiggle in one
of the regions ?
Sketch
Repeat here
Frame
?
?
Domain
Asymptotes
Periodicity
?
?
Repeat here
18
Wiggle
Derivative
2nd derivative