1. Section 2.3 Piecewise Defined Functions 2 Piecewise Defined Functions- when a function uses...
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Transcript of 1. Section 2.3 Piecewise Defined Functions 2 Piecewise Defined Functions- when a function uses...
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1
Powerpoint slides copied from or based upon:
Connally,
Hughes-Hallett,
Gleason, Et Al.
Copyright 2007 John Wiley & Sons, Inc.
Functions Modeling Change
A Preparation for Calculus
Third Edition
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Section 2.3
Piecewise Defined Functions
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Piecewise Defined Functions-
when a function uses different formulas on different parts of its domain.
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Piecewise Defined Functions-
when a function uses different formulas on different parts of its domain.
An example:
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Here is a graph of this piecewise function:
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Piecewise Defined Functions-
Another example:
g(x) = x + 1 for x ≤ 2 and
g(x) = 1 for x > 2
Let's graph this function:
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g(x) = x + 1 for x ≤ 2
andg(x) = 1 for x > 2
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes.
b. Graph the function.
c. State the domain and range of the function.
8Page 2 Example #2
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes.
99 for 0 < t 20( )
99 7( 20) for t > 20C f t
t
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You can simplify this expression to get:
99 for 0 < t 20( )
99 7( 20) for t > 20
99 for 0 < t 20( )
7 41 for t > 20
C f tt
C f tt
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But you lose the real meaning by doing so.
99 for 0 < t 20( )
99 7( 20) for t > 20C f t
t
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function.
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function.
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function.
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function.
Domain: t > 0 (call lengths ≤ 0 are silly)
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function.
Domain: t > 0 (call lengths ≤ 0 are silly)
Range?
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute.
Range?We can see that the range is:
C ≥ 99
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The Absolute Value Function
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The Absolute Value Function(defined piecewise):
for 0( )
for < 0
x xf x x
x x
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Some examples:
0 ?
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Some examples:
0 0
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Some examples:
5 ?
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Some examples:
5 ( 5) 5
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Let's form a table and then graph the absolute value function:
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x |x|−3 3−2 2−1 1 0 0 1 1 2 2 3 3
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This completes Section 2.3
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