Transcript domains of functions

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.
2x  3
g
x

• Ex.   x  7 Only the “x  7“ cannot equal 0.
• 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   2 x  18 , 2x 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!!!!  ,  