2.7 Piecewise Functions

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2.7 Piecewise Functions

• p. 114

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• Up to now, weve been looking at functions
  represented by a single equation.
• In real life, however, functions are represented
  by a combination of equations, each corresponding
  to a part of the domain.
• These are called piecewise functions.

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• One equation gives the value of f(x) when x 1
• And the other when xgt1

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Evaluate f(x) when x0, x2, x4

• First you have to figure out which equation to
  use
• You NEVER use both

X4
X2
X0 This one fits Into the top equation
So 2(4) 1 9 f(4) 9
So 022 f(0)2
This one fits here
So 2(2) 1 5 f(2) 5
This one fits here
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Graph

• For all xs lt 1, use the top graph (to the left
  of 1)
• For all xs 1, use the bottom graph (to the
• right of 1)

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x1 is the breaking point of the graph. To the
left is the top equation. To the right is
the bottom equation.
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Graph
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Step Functions
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Graph
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2.7 (continued)Writing Equations for Piecewise
Functions and Word Problems

• p. 115

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Writing a piecewise function given the graph.
The break in the graph Is at x0.
Notice where the circle dot are!!
To the left of x0 the graph is part of the line
thru (-2,0) (0,2)
y x 0 y x
An equation of this line is y x 2
y x 2
To the right of x0, the Graph is part of the
Line thru (0,0) (2,2)
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The piecewise function is
(open dot)
(closed dot)
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Write the equation of
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• You have a summer job that pays time and a half
  for overtime. (If you work more than 40 hours)
  After that it is 1.5 times your hourly rate of
  7.00/hr.
• Write and graph a piecewise function that gives
  your weekly pay P in terms of the number hours
  you work h.
• How much will you make if you work 45 hours?

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• From 0 to 40 hours you get 7.00/hr 7h
• over 40 you get
• 7(40) (1.5)(7)(h-40)
• 7(40) 10.5(h-40)
• 10.5h - 140
• The function is

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So the graph is
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• 2. P(h) 10.5h - 140
• P(45) 10.5(45) - 140
• 332.50 for 45 hours of work

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Assignment
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Assignment