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Piecewise Functions Guide

The document defines and provides examples of piecewise defined functions, which have different formulas on different parts of their domain. It evaluates piecewise functions at given values, defines the absolute value function as a piecewise function, and gives examples of evaluating and sketching graphs of absolute value and greatest integer functions. It also provides exercises involving computing values of piecewise functions and finding the Wind Chill Index given temperature and wind speed.

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Rafi Ano-os
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111 views11 pages

Piecewise Functions Guide

The document defines and provides examples of piecewise defined functions, which have different formulas on different parts of their domain. It evaluates piecewise functions at given values, defines the absolute value function as a piecewise function, and gives examples of evaluating and sketching graphs of absolute value and greatest integer functions. It also provides exercises involving computing values of piecewise functions and finding the Wind Chill Index given temperature and wind speed.

Uploaded by

Rafi Ano-os
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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FUNCTIONS

SPECIAL FUNCTIONS
OBJECTIVES:
• define piecewise defined functions;
• evaluate piecewise defined functions;
• enumerate some of the common functions that
can be defined as piecewise defined functions
• define absolute value function; and
• define greatest integer function

 
 

 
DEFINITION: PIECEWISE DEFINED FUNCTION
Sometimes a function is defined by more than one
rule or by different formulas. This function is called
a piecewise define function.
A piecewise defined function is defined by different
formulas on different parts of its domain.
Example: if
if x<0 if
if if
EXAMPLE:
A. Evaluate the piecewise function at the
indicated values.
if x<0 f(-2), f(-1), f(0), f(1), f(2)
if

if
if
if

f(-5), f(0), f(1),


f(5)
EXAMPLE:
B. Define g(x) = |x| as a piecewise defined
function and evaluate g(-2), g(0) and g(2).
Solution:
From the definition of |x|,
EXAMPLE:
Sketch the graph of the following functions and
determine the domain and range.
EXERCISES:
1.Compute the indicated values of the given functions.

a. b.

c.
2. Define H(x) as a piecewise defined function and
evaluate H(1), H(2), H(3), H(0) and H(-2) given by,

H(x) = x - |x – 2|.
3. For a given outside temperature T and wind speed v, the
Wind Chill Index (WCI) is the equivalent temperature that
exposed skin would feel with a wind speed of 4 mi/hr.
An empirical formula for the WCI based on experience
and observation is

where T is the air temperature in oF, v is the wind speed in


mi/hr, and WCI is the equivalent temperature in oF.
Find the WCI if the air temperature is 25oF and
a) v = 3 mi/hr,
b) v = 46 mi/hr and c) v= 15 mi/hr.
DEFINITION: ABSOLUTE VALUE FUNCTION
Recall that the absolute value or magnitude of
a real number is defined by

Properties of absolute value:


The graph of the function can be obtained
by graphing the two parts of the equation

separately. Combining the two parts produces the V-


shaped graph. It may help to generate the graph of
absolute value function by expressing the function without
using absolute values.
Example:
Sketch the graph of the following functions and determine
the domain and range.

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