Special Functions

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Special Functions

• Constant Function
• ex. y 4.95 The Charlies Smorgasbord
  Function
• Absolute Value Function
• ex. y x absolute Value
• Step (Greatest Integer) Function
• ex. y x The Bob Barker Price is
  Right Function
• Piece-wise Function
• ex. Made up of pieces!

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Lesson 6 Contents
Example 1 Step Function Example 2 Constant
Function Example 3 Absolute Value
Functions Example 4 Piecewise Function Example
5 Identify Functions
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Example 6-1a
Psychology One psychologist charges for
counseling sessions at the rate of 85 per hour
or any fraction thereof. Draw a graph that
represents this solution.
Explore The total charge must be a multiple of
85, so the graph will be the graph of a step
function. Plan If the session is greater than 0
hours, but less than or equal to 1 hour, the cost
is 85. If the time is greater than 1 hour, but
less than or equal to 2 hours, then the cost is
170, and so on.
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Example 6-1b
Solve Use the pattern of times and costs to
make a table, where x is the number of hours of
the session and C(x) is the total cost. Then draw
the graph.
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Example 6-1c
Examine Since the psychologist rounds any
fraction of an hour up to the next whole number,
each segment on the graph has a circle at the
left endpoint and a dot at the right endpoint.
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Example 6-1d
Sales The Daily Grind charges 1.25 per pound of
meat or any fraction thereof. Draw a graph that
represents this situation.
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Example 6-2a
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Example 6-2b
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Example 6-3a
Find several ordered pairs for each function.
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Example 6-3b
Graph the points and connect them.
Answer

• The domain of both graphs is all real numbers.

• The graphs have the same shape, but different
  x-intercepts.
• The graph of g (x) is the graph of f (x)
  translated left 5 units.

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Example 6-3c
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Example 6-4a
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Example 6-4b
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Example 6-4c
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Example 6-4d
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Example 6-5a
Determine whether the graphrepresents a step
function, a constant function, anabsolute value
function, or a piecewise function.
Answer Since this graphconsists of
differentrays and segments, it is a
piecewisefunction.
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Example 6-5b
Determine whether the graphrepresents a step
function, a constant function, anabsolute value
function, or a piecewise function.
Answer Since this graph is V-shaped, it is an
absolute value function.
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Example 6-5c
Answer absolute valuefunction
Answer constant function