Analyzing Functions and Graphs (day...
Transcript of Analyzing Functions and Graphs (day...
Analyzing Functions and Graphs (day 1).notebook
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January 24, 2014
Aug 2712:03 PM
Warm Up
1) Write the following in interval notation:
x < -12 or |x| < 5 or x 6
2) Write the following in interval notation, state whether the interval is boundedor unbounded and its type: x < 15
3) Graph the following equation, state whether it is a function andfind its domain and range. f(x) = x 2 - 4
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Analyzing Functions and Graphs
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Going more in depth with characteristics:
a) Domain and Rangeb) Continuityc) Extrema d) Increasing / Decreasing
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Domain and Range:
Two rules for domain: Not allowed to ________________________
Not allowed to have a __________________________
Example: f(x) =
Find the domain
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Find the Domain and Range of the following equation:
g(x) =
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b) ContinuityA function is continuous at x = a if
If this is not the case, then the function is discontinuous at x = a
Analyzing Functions and Graphs (day 1).notebook
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January 24, 2014
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Types of Discontinuity
Removable Discontinuity
Jump Discontinuity
Infinite Discontinuity
NonRemovable Discontinuity
Does the following equation have a discontinuity at the pointx = 0? If it does tell whether it is removable or non removable.
Example:
f(x) =
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c) Local and absolute extrema:
Local Max: Local Min:
Absolute Max:Absolute Min:
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(5,4)
(2,7)
(1,3)
(4,3)
x
y
Find the local and absolute max and min
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d) Increasing and Decreasing Functions:
Increasing has a ________________
Decreasing has a _________________
Constant interval has a __________________
ex) For the graph f(x) = |x 2| + |x + 5| 3
Find the intervals of inc/dec/constant
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