Daily Check

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Daily Check
Graph the following equations.
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Math II
UNIT QUESTION How are absolute value equations
similar to piecewise functions? Standard
MM2A1 Todays Question How are absolute value
equations similar to piecewise functions? Standard
MM2A1.a,b
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Absolute Value as Piecewise Functions

• Section 2.5

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Piecewise Functions

• Piecewise functions are functions that can be
  represented by more than one equation, with each
  equation corresponding to a different part of the
  domain.
• Piecewise functions do not always have to be line
  segments. The pieces could be pieces of any
  type of graph.
• This type of function is often used to represent
  real-life problems like ticket prices.

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Example
x 1, if x lt 1 2, if 1 x 3 (x-3)2 2,
if x gt 3
f (x)
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Absolute Value as Piecewise

• We usually write an absolute value function as f
  (x) x , but since absolute value is a measure of
  distance and distance is always positive, it also
  can be written as follows

-x, if x lt 0 x, if x 0
f (x)
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Writing Abs. Value as Piecewise

• For I x h I 0, simplify the equation given by
  distributing and combining like terms.
• For I x h I lt 0, substitute (x h) in place
  of I x - h I. Then, simplify.

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Example

• Write y 2 Ix 4I 10 as a piecewise function.
• For (x-4) 0
• 2(x 4) 10 2x 8 10 2x 18 (when x
  4)
• For (x-4) lt 0
• 2-(x-4) 10 2(-x 4) 10 -2x 8 10
• -2x 2 (when x lt 4))

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Graphs of Both
y2x-18
y-2x-2
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EOCT Practice
A
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EOCT Practice
C
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Writing Abs. Value as Piecewise

• Using a graph

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Writing Abs. Value as Piecewise

• Try this one...

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Practice

• Worksheet

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Homework

• Worksheet