Section 2.3 continued Linear Model Upgrades

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Section 2.3 (continued) Linear Model Upgrades
Piecewise-defined functions
Functions that are defined in several pieces
Ironman Triathlon Jasons DJ System Womens Shoe
Size Function
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Ironman Triathlon (pages 19, 76-77)
4K swim, 180K bike, 42K mile run
The table below summarizes the triathlon results
for one participant.
Assumptions for triathlon model
constant speed during each leg.
no time lapse between legs.
LEG 1 (4-0)/(1-0) 4 km/hr
LEG 2 (184-4)/(6-1) 36 km/hr
LEG 3 (226-184)/(10-6) 10.5 km/hr
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Ironman Triathlon (pages 19, 76-77)
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Ironman Triathlon (pages 19, 76-77)
What is the slope of each line?
m 4
m 36
m 10.5
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Ironman Triathlon (pages 19, 76-77)
What is the formula for each line?
S(t) 4t
B(t) 4 36(t-1)
R(t) 184 10.5(t-6)
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Ironman Triathlon (pages 19, 76-77)
What is the formula for the triathlon model?
PIECEWISE
4t for 0 t 1 4 36(t-1) for 1 4 10.5(t-6) for 6
T(t)
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Jasons 3000 DJ System Linear Depreciation L
(t) 3000 300t Double Declining Depreciation
D(t) 3000(.80)t
Jasons Best (Tax) Depreciation Model
PIECEWISE
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Womens Shoe Size Function w(x) 3x 21 domain
(continuous) 8.67 x 11.33
range (discrete) 5, 5.5, 6, 6.5, 7, 7.5, 8,
8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13
What is wrong with this graph?
when x 9 ¾, y ???
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Womens Shoe Size Function
piecewise defined
17 pieces !!(page 75)
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Homework Pages 85-87 45, 47-55 TURN IN 4
5, 52, 55 (maple graph)