DOMAINS OF FUNCTIONS

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					DOMAINS OF FUNCTIONS

    Chapter 1 material
        Restrictions of Domains
• (1) Does the function contain a fraction?
  – YES - go to FRACTION SLIDE
  – If no, continue with step (2) below
• (2) Does the function contain an even radical?
  – If yes, go to the RADICAL SLIDE
  – If no and the answer to (1) was no, GO TO SLIDE 5
  – If no but the answer to (1) was yes, the only
    restriction(s) you have is from the fraction.
               FRACTION SLIDE
• Since the bottom of the fraction can NEVER take
  the value ZERO, we should set the denominator
  equal to zero and solve. This will allow us to
  determine which values we CANNOT USE.
• Restrict the domain so that these values CANNOT
  BE USED.
• Ex. g  x   2xx73 Only the “  7“ cannot equal 0.
                                 x
• So x + 7 = 0 and x = -7. The domain is all real
  numbers EXCEPT -7!  , 7    7,  
• GO TO RESTRICTION SLIDE step 2
                RADICAL SLIDE
• The term (or expression) under the (even) radical
  MUST BE NON-NEGATIVE; i.e., it can be zero or positive
  and we will be able to obtain a real answer when we
  evaluate the radical.
• So, we set the term or expression GREATER THAN OR
  EQUAL TO ZERO and solve. The key here is knowing
  HOW to solve the inequality!
• Ex. f  x   2x 18 , 2 x  18  0 and then you MUST
  KNOW HOW TO SOLVE the inequality.
• In this example, you would add 18 to both sides and
  then divide each side by 2, obtaining x  9 as the
  restriction on the domain.
                    ANSWER
• You should determine how many restrictions you
  have based on your answers to the preceding
  questions.
• If you only had one restriction, simply put it into
  set notation.
• If you had more than one restriction, you should
  consider all numbers that will work as inputs
  from BOTH RESTRICTIONS…remember, the
  numbers must satisfy BOTH REQUIREMENTS
• Write your answer in set notation.
                   SLIDE 5
• If you reached this slide, the domain is ALL
  REAL NUMBERS!!!!  ,  

				
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posted:10/3/2011
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Jun Wang Jun Wang Dr
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