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. Only the “ “ cannot equal 0. So x + 7 = 0 and x = -7. The domain is all real numbers EXCEPT -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. , 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 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!!!!